microstructure characterization of ultra-fine grained cu-0
TRANSCRIPT
Microstructure
characterization of ultra-finegrained Cu-0.17wt%Zr
Von der Fakultät für Georessourcen und Materialtechnik
der Rheinisch-Westfälischen Technischen Hochschule Aachen
zur Erlangung des akademischen Grades eines
Doktors der Ingenieurwissenschaften
genehmigte Dissertation
vorgelegt von M.Sc.
Anahita Khorashadizadeh
aus Teheran
Berichter: Professor Dr.-Ing. Dierk Raabe
Univ.-Prof. Dr. rer. nat. Dr. h. c. Günter Gottstein
Tag der mündlichen Prüfung: 18. November 2011
Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar.
Shaker VerlagAachen 2012
Berichte aus der Materialwissenschaft
Anahita Khorashadizadeh
Microstructure characterizationof ultra-fine grained Cu-0.17wt%Zr
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Zugl.: D 82 (Diss. RWTH Aachen University, 2012)
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Meine Mutter und Maziar gewidmet.
Acknowledgement
The work presented in this thesis was carried out at the Max-Planck-Institute
for Iron research (MPIE) in Düsseldorf.
It is a pleasure to have the opportunity to thank all those who supported me
during this work.
My most sincere thanks go to Prof. Dr. Ing. Habil. Dierk Raabe. I thank
him for the time he always found for me for all scientific and non-scientific
discussions. I thank him for his unlimited encouragements, supports and pa-
tience during this work.
I would like to thank Univ.-Prof. Dr. rer. nat. Habil. Günter Gottstein for his
acceptance being the co-advisor of this work.
My heartfelt gratitude also goes to Priv. Doz. Dr. rer. nat. Habil. Myrjam
Winning. I thank her for her kind supervision and guidance during my thesis.
She always found time to listen to my questions. I thank her for her construc-
tive suggestions.
I am deeply grateful to Priv. Doz. Dr. Dip. Ing. Stefan Zaefferer for his help-
ful, inspiring and critical discussions. I thank him for sharing and teaching
me his knowledge in the field of microscopy and crystallography which was
of great importance for this work.
I also want to express my sincere gratitude to Prof. Gregory S. Rohrer and
Prof. Anthony D. Rollett for their support and training during my short stay
in Carnegie Mellon University and allowing me to use their algorithm for
characterizing the grain boundaries in 5-D space.
My thanks also go to all colleagues at the department of microstructure Physics
and Metal Forming at MPIE for the pleasant atmosphere which exist in the
group. My special thanks go to Mrs. Monika Nellessen and Ms. Katja An-
genent for their support in metallography, Mr. Herbert Faul and Mr. Frank
Schlüter for performing the heat treatment of the samples, Mr Achim Kuhl
and Mr. Berthold Beckschäfer for their support in IT field. I would like to
thank Dr. Alexander Kostka for his help to perform transmission electron
microscopy, Dr. Ing. Claudio Zambaldi and MSc. Nima Hamidi for their
help and support for using LaTex and MSc. Farangis Ram for her linguistic
corrections.
My special thanks go to Dr. rer. nat. Olga Dmitrieva and Dipl. Ing. Nahid-
Nora Elhami for their friendship and the nice working atmosphere.
I would like to express my eternal thanks to my mother because of her ev-
erlasting support and love. Finally I would like to thank Dipl. Inf. Maziar
Khodaei with all my heart for his patience and encouragements during this
work.
vi
Contents
1 Introduction 1
2 Background 72.1 plastic deformation of metals . . . . . . . . . . . . . . . . . 7
2.1.1 Grain refinement . . . . . . . . . . . . . . . . . . . 10
2.1.2 Severe plastic deformation . . . . . . . . . . . . . . 11
2.2 Softening Processes . . . . . . . . . . . . . . . . . . . . . . 22
2.2.1 Recovery . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.2 Primary recrystallization . . . . . . . . . . . . . . . 22
2.2.3 Grain growth . . . . . . . . . . . . . . . . . . . . . 25
2.2.4 Softening processes after very large plastic strains . 26
2.3 Grain boundaries . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 General concepts of EBSD . . . . . . . . . . . . . . . . . . 27
2.4.1 Automated evaluation of EBSD patterns . . . . . . . 28
2.4.2 Spatial and angular resolution . . . . . . . . . . . . 30
2.5 Principle of the transmission electron micros-copy . . . . . . 31
2.6 CuZr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 Experiments 353.1 Sample processing . . . . . . . . . . . . . . . . . . . . . . 35
3.1.1 Equal channel angular pressure deformation . . . . . 35
3.1.2 High pressure torsion deformation . . . . . . . . . . 35
vii
Contents
3.1.3 Annealing . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 Microstructure characterization . . . . . . . . . . . . . . . . 37
3.2.1 2D- EBSD- based orientation experiments . . . . . . 37
3.2.2 3D- EBSD- based orientation experiments . . . . . . 38
3.2.3 Transmission electron microscopy . . . . . . . . . . 42
3.2.4 Hardness measurements . . . . . . . . . . . . . . . 42
4 Recrystallization behavior of ultra-fine grained Cu-Zr alloy 454.1 Microstructure characterization . . . . . . . . . . . . . . . . 46
4.1.1 Deformed state subjected to high pressure torsion . . 46
4.1.2 Annealed state after subjection to high pressure torsion 54
4.1.3 Results and Discussion . . . . . . . . . . . . . . . . 59
4.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5 3-D Microstructure 795.1 3-D based microstructure and microtexture characterization . 79
5.1.1 Deformed state subjected to equal channel angular
pressing . . . . . . . . . . . . . . . . . . . . . . . 80
5.2 Grain boundary analysis . . . . . . . . . . . . . . . . . . . 108
5.2.1 Grain boundary character distribution . . . . . . . . 113
5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Summary 129
Zusammenfassung 133
Curriculum vitae 146
viii
1
Introduction
Ultrafine-grained (UFG) materials can be defined as polycrystalline materials
with submicrometer, 100− 1000 nm, or nanometer, less than 100 nm, average
grain sizes. In addition to their high toughness and a long fatigue life, UFG
materials possess substantially improved combination of yield strength and
ductility over the conventional coarse-grained materials (fig. 1.1). Although
these materials are still in the incubation period of their commercial life, they
have already found their ways into some specific application areas, e.g. UFG
Ti alloys, NiTi shape-memory alloys and austenitic steels in implants and
tools used in medicine, and UFG NiTi shape-memory alloys in parts of ther-
momechanical clutches in automative industry (1). Such materials with good
mechanical properties are more attractive for practical applications, if the mi-
crostructure is stable enough at higher application temperatures in order that
they retain their mechanical properties at elevated temperatures.
The bulk ultrafine-grained materials can be produced by severe plastic defor-
mation (SPD) methods. Numerous techniques have been established for the
fabrication of UFG materials which are all based on SPD methods, among
which Equal channel angular pressing (ECAP), high pressure torsion (HPT),
multidirectional forging (MDF), twist extrusion (TE), and accumulative roll
1
Fig. 1.1: Strength and ductility of nanostructured metals compared with
coarse-grained metals (2).
2
1. Introduction
banding (ARB) play the leading role. A unique feature of SPD processing
is the imposition of higher levels of strain without significant changes in the
overall dimensions of the workpiece (3). UFG materials should exhibit a high
thermal stability is indispensable since otherwise they lose their superior me-
chanical properties during production or application due to the coarsening of
the microstructure. There are rarely studies performed on annealing behavior
of nanostructured materials produced by SPD methods (4, 5, 6, 7, 8, 9, 10).
In ultra fine grained materials during deformation or successive annealing
processes a bimodal microstructure develops, which can be referred to as
discontinuous recrystallization or discontinuous grain growth. Distinction in
the physical interpretation of these two procedures is of great importance.
The discontinuous recrystallization gains its driving force from the stored
energy of the dislocations produced during deformation, and discontinuous
grain growth is curvature driven. Molodova et al. (7) have investigated the re-
crystallization behavior of the Cu-0.17wt%Zr alloy on annealing after ECAP.
The amount of high angle grain boundaries in the microstructure after 12
number of ECAP passes was about 70% . In this project the aim is to inves-
tigate the microstructure of Cu-0.17wt%Zr with higher fraction of high angle
grain boundaries which will be induced in the microstructure via high pres-
sure torsion (HPT) method. According to an investigation by Humphreys et
al. over 70% area fraction of high angle grain boundaries in the microstruc-
ture is enough to stabilize the microstructure against the discontinuous growth
at higher temperatures. Therefore one part of this project is dedicated to the
investigated the behavior of ultrafine-grained Cu-0.17wt%Zr alloy on sub-
sequent annealing after high pressure torsion deformation at large strains
(ε ∼ 4 − 27). Due to low solubility of Zr in Cu at room temperature elec-
trical conductivity of about 85-95% IACS (International Annealed Copper
Standard) in the aged and 55-72% IACS in the solution annealed stated can
be obtained in Cu-0.17wt%Zr alloy which also is thermally more stable at
elevated temperatures compared to pure Cu. Processing of such alloy with
SPD methods increases their strength, which makes this alloys attractive in
practical applications.
In this study at first, the micro -structure and -texture evolution of Cu-
0.17wt%Zr alloy in deformed state will be characterized . The characteri-
3
zation of the deformed structure is of great importance since it affects the
recrystallization behavior of these materials. The measurements will be per-
formed by 2D electron back scatter diffraction (EBSD), transmission electron
microscopy (TEM) and hardness measurements . Subsequently the behavior
of the material under heat treatment will be analyzed by performing series
of annealing experiments. 2D EBSD, transmission electron microscopy and
hardness measurements will be executed for the characterization of the mi-
crostructure and texture evolution of the annealed state.
The motion of grain boundaries is the key phenomenon for recrystallization
and grain growth. In order to clarify the recrystallization behavior of UFG
materials, it is of great interest to investigate the grain boundary structure.
Grain boundary motion generally depends on different parameters, e.g. the
lattice defects (impurities, vacancies, and dislocations); the grain boundary
structure, which varies in a 5D parameter space as a function of misorien-
tation (3 variables); and the grain boundary plane orientation (2 variables).
Grain boundary structure can be analyzed by the grain boundary character
distributions (GBCD) in crystalline materials. The 5D GBCD specifies the
fractions of interface area sections, classified according to the 3 lattice mis-
orientation parameters and the 2 grain boundary normal parameters. GBCD
can be obtained in two ways, namely, applying the statistical-based stereo-
logical approach on 2D EBSD measurements (11, 12), or analyzing of every
individual boundary in the microstructure measured by 3D EBSD (13). The
advantage of latter approach over the former is avoiding the statistical ruling
out risk. To calculation the GBCD large number of grain boundary segments
(12) in the microstructure is necessary. Since the ultrafine-grained materials
provide a large number of grains which can be measured in the volume mea-
sured by 3D EBSD (50[μm]3), the microstructure is suitable for executing the
serial sectioning for 3D EBSD and subsequent GBCD analysis. Up to now
there are no studies on 3D microstructure of the ultrafine-grained materials
processed by SPD methods. The 3D EBSD method leads to a better under-
standing of the origin of the 3D heterogeneity of the spatial distribution and
connectivity of the main texture components, texture gradients, and interfaces
as well as information on the 5 parameter grain boundaries produced by SPD
processing. The second part of the project is dedicated to the investigation
4
1. Introduction
of the 3D microstructure. The most important aim of this part beside 3D
characterization is to find out if the information from the 3D EBSD approach
cannot be obtained from the 2D measurements for the complicated structures
developed during deformation of the materials by SPD methods, here ECAP
method. 3D EBSD measurements are carried out by a combination of a fo-
cused ion beam (FIB) system and a high resolution field emission scanning
electron microscope.
5
2
Background
2.1 plastic deformation of metals
Metals can undergo high plastic deformations because of their high ductility.
Crystallographic slip is by far the most important and dominant deforma-
tion mechanism in ductile materials. There are also other options for plastic
deformation without changing the crystal structure, namely a shape change
by diffusion or mechanical twinning. Diffusion plays an important role in
the high temperature creep, while twinning is particularly important during
low temperature deformation in metals with low stacking fault energy (SFE)
(14). During elastic deformation the crystal changes its structure, while dur-
ing plastic deformation the crystal structure does not change. A conservation
of crystal structure with external change is only possible if complete blocks of
a crystal are translated parallel to crystallographic planes (fig. 2.1). To move
a dislocation on its slip plane through the crystal lattice a force is required,
which is called Peierls-Nabarro force:
τp =2G
1 − ν exp(−2π
1 − νdb
) (2.1)
7
2.1. plastic deformation of metals
Fig. 2.1: Plastic deformation of crystals (dashed lines = unit cell). a) by
changing the crystal structure, b) without changing the crystal structure
(14).
where d is the distance between slip planes and b is the distance between
atoms in the slip direction (Burgers vector). In face-centered cubic (FCC)
metals the spacing between {111} planes is the largest and the spacing of the
atoms is smallest along <110> direction. τp decreases with increasing d and
decreasing b. Slip system in FCC metals seems to process on {111} planes
and <110> directions. In FCC metals there are 12 possible slip systems.
Normally the measured ritical resolved shear stress is smaller than the one
calculated from the Peach-Kohler equation (equation 2.1). This is due to ne-
glecting the thermal activation. The dynamic of the deformation is described
by Orowan equation:
γ = ρmbϑ (2.2)
where ρm is the mobile dislocation density and ϑ is the average speed of the
dislocations. The Orowan equation provides the relation between the macro-
scopic strain and the microscopic mechanism of deformation.
The change of shape associated with twinning is due to simple shear in which
8
2. Background
a volume fraction of crystal changes its orientation into an orientation with
mirror symmetry relative to the parent matrix. Twinning is characterized by
the twinning plane and the direction of shear. For FCC metals the twinning
system is {111}<112>. Twinning generally occurs when the slip systems are
restricted or the critical resolved shear stress increases so that the twinning
stress (γt =√
2/2) is lower than the stress for slip. Due to this fact the twin-
ning occurs at low temperatures or high strain rates in body-centered cubic
(BCC) and FCC metals or in at hexagonal closest packing (HCP) metals at
orientations which are not suitable for basal slip (15).
One of the chief characteristics of plastic deformation is that the shear stress
required to produce slip increases with increasing shear strain. Increase of
the shear stress is called strain hardening or work hardening. Work hard-
ening occurs in metals because of the interaction of dislocations with one
another and also with barriers which impede the movement of the disloca-
tions through crystal. Dislocation multiplication can arise from regeneration
under applied stress from existing dislocations by Frank-Read mechanism,
by a multiple cross-slip mechanism or by emission of dislocations from high-
angle grain boundaries (15). Numerous studies in the mechanical properties
of single crystals have shown that the stress-strain curve of the single crys-
tals is divided into three stages (fig. 2.2). Stage I occurs only during single
slip in single crystals. During this stage dislocations move long distances in
the crystal when the flow stress reaches and exceeds τ0. Stage II occurs be-
cause of the reaction of primary dislocations with dislocations on secondary
slip systems, which provide immobile dislocations and can not be overcome
by the successive dislocations. This leads to increase of internal stresses and
create a large activity of secondary slip systems. During this stage dislocation
density increases while for each immobile dislocation another mobile dislo-
cation should be generated to maintain the rate of imposed strain. Increase
of dislocation density leads into increase of flow stress to maintain plastic
deformation. The rate of strain hardening is independent of the crystal ori-
entation and structure and is approximately about G300
. Stage III starts after
the shear stress τIII is reached. In this stage the strength continues to increase
but the strain rate decreases. This stage is the longest stage of the hardening
curve. During this stage cross slip is gradually established. Studies on stage
9
2.1. plastic deformation of metals
Fig. 2.2: Schematic hardening curve of FCC single crystals oriented for sin-
gle slip (14).
IV was performed by Langford and Cohen (16) and Kuhlmann-Wilsdorf and
Hansen (17). Kuhlmann-Wilsdorf and Hansen (17) defined the stage IV as a
work-hardening stage within which large plastic strains can occur at a very
low, constant work-hardening rate. Although stages II and IV exhibit constant
work-hardening rate, they differ, because in stage II, cross slip is insignificant,
while in stage IV, it is unlimited (17). Stages V and VI may follow through
establishment of climb (17).
2.1.1 Grain refinement
Deformation of the metals leads to changes in the microstructure and micro-
texture. The mechanical properties of materials are determined by several fac-
tors, one of the most important factors is the average grain size. The strength
of materials is directly related to the grain size according to the Hall-Petch
10
2. Background
equation (18, 19):
σ = σ0 + Kyd−12 (2.3)
where σ is the yield strength, d grain size and Ky a constant of yielding.
The equation shows that with reduction in grain size, the strength increases.
The commercial deformation approaches can not be used to produce submi-
crometer grain sizes. Accordingly the attention towards the techniques which
can produce ultrafine grained materials with grain sizes in submicrometer
and nanometer ranges increased (20). Two basic approaches are developed
for producing the ultrafine grained materials, namely the bottom-up and top-
down approaches. In the bottom-up approaches, e.g. inert gas condensation
(21, 22), electrodeposition (23), ball milling (24), synthesize the ultrafine
grained materials by assembling atoms or by consolidating nanoparticulate
solids. At present these procedures are expensive and not possible for pro-
duction of industrial applications in large scales. Another feature of such ma-
terials is the contamination in material. In Top-down approaches the coarse
grain size materials are subjected to heavy straining or shock loading. This
approach does not suffer under small sizes of the products and also the con-
tamination of the material. Severe plastic deformation methods is included in
the Top-down approaches.
2.1.2 Severe plastic deformation
Sever plastic deformation(SPD) methods produce ultra fine-grained materi-
als (with grain sizes in the range of 100nm-1μm) by imposing very high
strains on materials, which reveal extraordinary properties, such as ultra high-
strength and high ductility (25, 26, 27, 2). The unique feature of SPD meth-
ods is that high strains are imposed at low temperatures and the dimension of
the workpieces executed to high strains are without significant changes, also
the shape of the workpieces is retained during the severe plastic deformation
(3). The most common SPD approaches are equal channel angular pressing
(ECAP) (fig. 2.3) , high pressure torsion (HPT) (fig. 2.4), accumulative roll
bonding (ARB) (fig. 2.5) (28, 29, 30).
The advantage of the SPD methods is that the dimensions of the samples
11
2.1. plastic deformation of metals
Fig. 2.3: Schematic illustration of equal channel angular pressure (20).
during deformation are almost without changes, which makes it possible to
repeat the deformation many times and reach higher amounts of strain.
Equal channel angular pressing
The ECAP process consists of two equal cross section channels, intersecting
at an angle φ (fig. 2.3). A rod is pressed through the ECAP die, so that the
material deforms via simple shear at the intersection plane of the two channels
(20). There are different ECAP routes, namely route A, BA, BC and C. In
route A the sample is processed repetitively without any rotations, in route BA
12
2. Background
Fig. 2.4: Schematic illustration of a high pressure torsion method (31).
Fig. 2.5: Schematic illustration of accumulative roll bonding (28).
13
2.1. plastic deformation of metals
Fig. 2.6: Schematic illustration of shearing in a single pressing through the
die: X, Y and Z define three orthogonal planes of observation (34).
the sample is rotated by 90◦ in alternative directions between passes, in route
BC the sample is rotated by 90◦ around the longitudinal axis in the same sense
between ECAP passes and in route C the sample is rotated by 180◦ between
passes. Table 2.1 illustrates the effect of pressing with different routes on the
consequent shearing of the cubic element shown in fig. 2.6. RouteA leads
to distortions in the X and Y planes but no deformation in Z plane, route
BA leads to distortions on all three planes and in route BC and route C the
cubic element is restored every four and two pressings, respectively. For the
channel angle of φ = 90◦ route BC is generally the most expeditious method
for developing the UFG structure (32, 33). Different routes affect the changes
in the microtexture and microstructure due to different shear planes (34).
The equivalent strain from the ECAP deformation can be calculated from the
following equation:
14
2. Background
Tab. 2.1: Shearing characteristics for six different processing routes (34).
15
2.1. plastic deformation of metals
ε =2√3
cot(φ
2) (2.4)
where φ is the angle between two intersecting channels. The shear strain after
one ECAP pass with ECAP die angle of 90◦ is about 1.15. In ECAP pro-
cessing the material can undergo very high strains by repetitive pressing. In
this procedure the subgrain boundaries tend to gradually form into high grain
boundaries through accumulation and absorption of dislocations (35). This
procedure produces ultrafine grains that are separated by high angle grain
boundaries. In ECAP processing route BC is the most effective route for pro-
ducing ultra fine grains (35, 36, 32). The grain size after several ECAP passes
may be defined after one ECAP pass, which corresponds to the width of the
elongated grains (37).
As mentioned before in the ECAP process the material deforms through sim-
ple shear deformation. The common texture components develop during de-
formation are the ideal shear texture components with deviations from their
ideal position. The ECAP texture are presented in the X-Y-Z coordinate sys-
tem (fig. 2.7) shear deformation is indicated by the X′ − Y′ − Z′ coordinates.
The shear plane is parallel to the X′ − Y′ plane (35). The system should be
rotated 45◦ in order to have the shear texture components in X-Y-Z coordinate
system (for the channel angle φ = 90◦). In table 2.2 the ideal ECAP texture
components of FCC materials are represented.
The texture evolution in ECAP materials has been investigated experimen-
tally using X-ray diffraction (XRD) and electron back scatter diffraction (EBSD)
methods (7, 38, 39) as well as theoretically by micromechanical simulations
(38, 40, 41, 42). The mechanical origin of texture evolution and inhomo-
geneity resulting from ECAP can be studied using crystal mechanical mod-
els: for instance Gholinia et al. (38) modeled the deformation texture in alu-
minium during ECAP using a full constraints Taylor approach. They also in-
vestigated the texture experimentally via EBSD. The textures observed in the
16
2. Background
Tab. 2.2: The main ideal texture components of simple shear textures for
face centered cubic (FCC) metals in the ϕ2 = 45◦ section in Bunge
Euler space.
Texture Euler angles Miller indices
component ϕ1 φ ϕ2 {hkl} < uvw >
AE 45◦ 35.26◦ 45◦ (9 1 4) < 1 11 5 >
AE 225◦ 35.26◦ 45◦ (11 1 4) < 1 9 4 >
BE 45◦ 54.74◦ 45◦ (15 4 11) < 7 26 19 >165◦ 54.74◦ 45◦285◦ 54.74◦ 45◦
BE 105◦ 54.74◦ 45◦ (7 26 19) < 15 4 11 >225◦ 54.74◦ 45◦345◦ 54.74◦ 45◦
CE 45◦ 90◦ 45◦ (3 3 4) < 2 2 3 >225◦ 90◦ 45◦
A∗1E 170.37◦ 90◦ 45◦ (1 1 8) < 4 4 1 >350.37◦ 90◦ 45◦
A∗2E 99.74◦ 90◦ 45◦ (4 4 1) < 1 1 8 >279.74◦ 90◦ 45◦
17
2.1. plastic deformation of metals
Fig. 2.7: Schematic image of the ECAP die (φ = 90◦) together with the
relevant coordinate systems. The X-Y-Z system represents the ECAP
reference system used for the texture analysis whereas the X′ − Y′ − Z′coordinate system represents the ideal shear reference systems.
experiments had the main components {001}<110> and {112}<110> along
a partial B texture fiber (characterized by {hkl}<110>) rotated by 15◦-20◦about the transverse direction (TD). The TD rotation was successfully pre-
dicted by the full constraint Taylor model (38). The {001}<110> texture
components in FCC metals are stabilized by strong shear processed while
under plane strain loads they are highly unstable (43, 44, 45). Toth et al.
(40) used the flow line approach in conjunction with a viscoplastic Taylor
model and a viscoplastic self-consistent polycrystal plasticity model to simu-
late ECAP deformation textures. The orientation distribution function (ODF)
predicted were similar to those observed for simple shear experiments with
relatively small deviations to the ideal shear positions. Using a viscoplastic
self-consistent approach Beyerlein et al. (41) developed a modeling frame-
work for predicting the microstructure and texture evolution in polycrystalline
materials during ECAP processing. They found that the main microstructural
features such as grain size and grain shape distribution as well as texture
were dependent on the processing route. Molodova et al. (7) investigated
the microstructure and texture evolution of pure copper (99.95%) after ECAP
processing using X-ray diffraction methods. They observed that simple shear
18
2. Background
components were developed during deformation. After higher numbers of
ECAP passes (ECAP12) the strongest component was an orientation between
(15 4 11) < 7 26 19 > and (3 3 4) < 2 2 3 >.
High pressure torsion
Fig. 2.4 schematically shows the principle of the HPT processing. The sam-
ples in the form of disk are located between two anvils and one of the anvils
is rotated against the other one which leads to a torsional strain parallel to a
compressive applied pressure of several GPa (46, 31). The equivalent strain
imposed in HPT process can be estimated from the following equation:
ε = ln(2πNr
h) (2.5)
where N is the number of revolutions, r the radius of the disk and h the
thickness of the disk. The strain along the radius of the sample is not constant
and increases with increasing the radius. Earlier studies suggested that HPT
may be more effective in producing small grain sizes than ECAP. Whereas the
ECAP process produces UFG materials with grain sized in range f 100-1000
nm, several reports demonstrate grain sizes smaller than 100 nm in materi-
als processed by HPT. Lugo et al. (47) have investigated the smallest grain
size achieved in ECAP and HPT process on pure copper. The pure copper
samples were processed by 8 ECAP passes via route BC and HPT processing
was conducted under an applied pressure of 6GPa with 5 rotations. It was
claimed from TEM micrographs that the grain size of the ECAPed samples
range between 150-300 nm and the grain size distribution was almost homo-
geneous and no evidence of recrystallization was found. They found out that
the samples processed by HPT had a bimodal distribution, i.e. grains with
sizes lying between 100-300 nm and coarse defect-free grains with sized be-
tween 800 and 1200 nm. It was claimed that these grains were developed
during deformation due to the heat generated during deformation and inher-
ent nature of stacking fault energy materials. Islamgaliev et al. studied the
microstructure evolution of CP Ti subjected to HPT under an applied pressure
of 6GPa with the number of rotations of 10. The grain size achieved ranged
19
2.1. plastic deformation of metals
between 105-120 nm and reached an ultimate tensile strength up to 1600 MPa
(48). Zhilyaev et al. (49) subjected the pure nickel samples to 3 different se-
vere plastic deformation methods: ECAP, HPT and ECAP+HPT. The results
showed the mean grain size is largest after ECAP, intermediate after HPT and
the smallest grain sizes of about 140nm was achieved after a combination of
ECAP and HPT. They suggested processing of materials through a combina-
tion of ECAP followed by HPT. Pippan et al. (50) investigated the limits of
the structural refinement during HPT deformation. The single phase materials
revealed a relatively uniform behavior, i.e. a decrease in the grain size was
observed with increasing the misorientation between neighboring elements
and saturation of refinement was achieved between an equivalent strain of 5
and 50. They attributed a more complex behavior of the multi-phase mate-
rials under severe plastic deformations. The thermal stability of pure copper
was investigated by Jiang et al. (51). They observed a very low thermal sta-
bility of HPT-processed copper. The texture components developed during
HPT deformation are represented by ideal shear texture components shown
in table 2.3. Two texture fibers forms during HPT, namely {111}<uvw> and
{hkl}<110> (52, 53). Generally there are less studies on the texture devel-
opment after HPT processing. Alexandrov et al. (53) investigated the de-
velopment of crystallographic texture in copper subjected to high pressure
torsion experimentally. Their experimental analysis of texture based on X-
ray diffraction method. They found out that after first rotation at areas near
to the center of the disc the strongest texture components were the C and A∗,while at larger distances from the center of the sample the intensity of the A
and B components increased. They observed that with increasing the number
of rotations the intensity of dominating texture component decreases which
was attributed to the contribution of grain boundaries at higher deformation
degrees.
20
2. Background
Tab. 2.3: The main ideal texture components of ECAP textures for face cen-
tered cubic (FCC) metals in the ϕ2 = 45◦ section in Bunge Euler space
Texture Euler angles Miller indices
component ϕ1 φ ϕ2 {hkl} < uvw >
A 0◦ 35.26◦ 45◦ (1 1 1) < 1 1 0 >
A 180◦ 35.26◦ 45◦ (1 1 1) < 1 1 0 >
B 0◦ 54.74◦ 45◦ (1 1 2) < 1 1 0 >120◦ 54.74◦ 45◦240◦ 54.74◦ 45◦
B 60◦ 54.74◦ 45◦ (1 1 2) < 1 1 0 >180◦ 54.74◦ 45◦300◦ 54.74◦ 45◦
C 0◦ 90◦ 45◦ (1 0 0) < 0 1 1 >180◦ 45◦ 45◦
A∗1 125.37◦ 90◦ 45◦ (1 1 1) < 2 1 1 >305.37◦ 90◦ 45◦
A∗2 54.74◦ 90◦ 45◦ (1 1 1) < 2 2 1 >234.74◦ 90◦ 45◦
21
2.2. Softening Processes
2.2 Softening ProcessesAfter deformation the material includes high densities of dislocations and
grain boundaries, which make the material thermodynamically unstable. At
room temperature the material is mechanically stable so that the defects do not
disappear but with increasing the temperature the defects may be removed due
to thermally activated processes, which bring the material in a lower energy
configuration. The annealing processes which lead to removing the defects
from the microstructure of the material are recovery, primary recrystallization
and grain growth.
2.2.1 Recovery
During recovery changes occur in the material which partially restores the
properties of the material to the values before deformation. The recovery pro-
cess is prior to the recrystallization process.The changes in the microstructure
are due to the changes of the dislocation structure of the materials. Recovery
is referred to processes which are associated with rearrangement or annihila-
tion of dislocations (14). Fig. 2.8 shows different steps taking place during
recovery (54). Recovery depends on many parameters, namely annealing
temperature, purity of material, strain and deformation temperature (54).
2.2.2 Primary recrystallization
Primary recrystallization during annealing refers to a process in which the
new defect free grains form and these grains grow so that they consume the
deformed structure. During recrystallization the microstructure is divided into
two areas, the defect-free areas and the deformed structure. The primary re-
crystallization is also called discontinuous recrystallization since the removal
of dislocations in the microstructure is not homogeneous. Primary recrys-
tallization is characterized by nucleation and nucleus growth. According to
Humphreys (54) the term nucleation is not the appropriate term since nu-
cleation in the classic thermodynamics does not occur. The proper term for
22
2. Background
Fig. 2.8: Different stages in recovery of deformed materials (54).
23
2.2. Softening Processes
the nucleation would be the initiation (54). Nuclei are the areas which have
low internal energy area and grow into the deformed structure. The driving
force of the primary dislocations is from the stored energy of the dislocations:
P =1
2ρGb2 (2.6)
where P is the driving force, G the shear modulus and b the Burgers vector. If
the small grain of radius R grows in the deformed microstructure, an opposing
force comes from the curvature of grain boundaries with a specific energy of
γb:
Pc =2γb
R(2.7)
The minimum size of the nucleus should be at least 1 μm for the grain bound-
ary energy of 0.5 Jm−2 so that the nucleus is able to grow (where Pc is equal
to Pd). Other parameters which can affect the recrystallization behavior of
a metal are the retarding forces from solid solutes and also from the second
phase particles. The kinetics of recrystallization are described in terms of a
recrystallization temperature, at which the recrystallization is complete in a
in commercially realized time (typically 1 hour) (14). Recrystallization is de-
pendent on temperature and small temperature variations changes the time of
recrystallization. The fraction of recrystallized microstructure can be calcu-
lated from the Johnson-Mehl-Avrami-Kolmogorov equation (14):
X = 1 − exp{−(ttR
)q} (2.8)
where X the recrystallized volume fraction, t annealing time, tR (X(tR) =
0.63) characteristic time for recrystallization and q the time exponent. From
the hardness measurements the recrystallized volume fraction of the material
can be calculated. Under assumptions that the nucleation occurs homoge-
neously and nucleation rate (N) and growth rate (v) are constant during the
recrystallization, the recrystallized fraction can be calculated from:
tR = (π
3Nv3)−
14 (2.9)
24
2. Background
where:
v = v0exp(− Qv
kBT) (2.10)
N = N0exp(− QN
kBT) (2.11)
The apparent activation energy of the primary recrystallization (QR) can be
calculated from
tR =3
πN0v03
14
.exp(QN + 3Qv
4kBT) (2.12)
or
tR ≈ exp(QR
kBT) (2.13)
2.2.3 Grain growthAfter primary recrystallization whose driving force is from the stored energy
of dislocations, the microstructure is still not stable due to the presence of
grain boundaries. Further growth of the recrystallized grains occur leading to
reducing of the energy which is stored in grain boundaries. The driving force
of the grain growth is normally two orders of magnitude smaller than the driv-
ing force of the primary recrystallization. The parameters which may affect
the grain growth are: temperature, solutes and particles, specimen size and
texture (54). The grain growth process can be divided in two types, namely
the normal grain growth and abnormal grain growth. In the normal grain
growth the coarsening of the microstructure occurs homogeneously, while in
abnormal grain growth some grains grow and consume the microstructure.
The theory of Burke and Turnbull (55, 56) for the kinetic of grain growth is
based on the assumption that the driving force of the normal grain growth
comes from the curvature of the boundaries (equation 2.7). The Kinetic of
growth according to Burke and Turnbull (55, 56) can be calculated as follow-
ing:
25
2.2. Softening Processes
R 2 − R02 = c2t (2.14)
Where R is the mean grain size at time t, R0 is the starting mean grain size
and c2 is a constant.
The driving force of the abnormal grain growth is:
P =3γ
R(2.15)
where γ is the special energy of the grain boundaries and R the grain size of
the grains.
2.2.4 Softening processes after very large plastic strainsThere are some studies showing that the microstructure of largely strained
materials are resistant against recrystallization (57, 58, 59). According to
Humphreys (57) with increasing the average misorientation, the stability of
the microstructure increases. At sufficiently large strains the area fraction of
high angle grain boundaries and hence the mean misorientation of the mi-
crostructure increases. The model developed by Humphrey (57) predicted
that the area fraction of high angle grain boundaries should be ≈ 0.6 − 0.7 to
prevent discontinuous recrystallization. Fine grained materials have a large
stored energy due to the high fraction of high angle grain boundaries, which
may undergo a grain growth on annealing at higher temperatures. Engler and
Huh (58) investigated a microstructure heavily deformed by cold rolling. The
microstructure recrystallized continuously and on further annealing it showed
abnormal grain growth. Hayes et al. investigated the microstructure of a Al-
Mg alloy deformed by sever plastic deformation methods, which underwent
a normal grain growth (60). Presence of second phase particles affect the nor-
mal or abnormal grain growth of a fine grained microstructure. Humphreys et
al (61) predicted the influence of pinning particles ( Fvd ), where Fv is the frac-
tion of second phase particles and d is the mean size of the second phase par-
ticles, and grain size on the stability of the microstructure. It was discussed
that with increasing of Fvd the abnormal grain growth will be prevented for
larger grains but abnormal growth is likely for the smaller grains (61).
26
2. Background
2.3 Grain boundaries
Grain boundaries are two dimensional planar defects in crystalline materials
which separate two crystals of the same structure but of different orienta-
tion. In three dimensional space 8 parameters are needed to characterize the
boundaries mathematically. Three parameters for the misorientation (orien-
tation relationship of two neighboring crystals) and three parameters of the
normal of the grain boundary planes and finally the translation vector. These
parameters affect the energy and mobility of the grain boundaries. The trans-
lation vector of the boundaries.Five of these parameters can be influenced
externally, namely the orientation relationship and the spatial orientation of
grain boundaries. The Wulff plot represents the relation of the orientation of
grain boundary plane with grain boundary energy. Grain boundaries tend to
align themselves parallel to orientations with lower energies, such as coherent
twin boundaries. There are two types of grain boundaries, namely tilt bound-
aries and twist boundaries. In tilt boundaries the rotation axis is parallel to the
boundary plane, if two adjacent crystals have mirror symmetry then the grain
boundary is called symmetric tilt boundaries and all other tilt boundaries are
called asymmetric tilt boundaries. Twist boundaries are boundaries whose
rotation axis is perpendicular to the boundary plane.
2.4 General concepts of EBSD
To obtain the orientation information of microstructure the size of the probe
should be smaller than the microstructural units themselves. Electrons are
ideal for characterizing the microstructure and microtexture of the materials
(62). The electron back scatter diffraction (EBSD) method is developed for
this purpose (63, 64). The EBSD technique can be used for all microtextural
studies, phase identifications and also strain measurements. This technique
makes it possible to perform rapid, automatic diffraction analysis to obtain
crystallographic data with spatial resolution of less than 0.5μm. The principle
of the EBSD measurements are based on electrons entering into the crystal.
The electrons scatter incoherently in the crystal (62, 65) and form an electron
27
2.4. General concepts of EBSD
source inside of the crystal. These electrons might be diffracted on the lattice
planes according to Bragg equation (equation 2.16).
nλ = 2d sin θ (2.16)
where λ is the wave length of incident electrons, d: the distance between
lattice planes and θ : is the angle between the incident electrons and the scat-
tering planes. For most crystal structures, reflection from all lattice planes is
not possible. For BCC crystal structures the reflection of the lattice planes
can be observed whose sum over all Miller indices (h, k, l) is odd and in FCC
crystal structures reflection is observed when the Miller indices (h, k, l) are
either all odd or all even. It can be see in fig. 2.9 that the diffracted electrons
from a point source inside of the crystal form 2 cones with an opening angle
of 180◦ − 2θ which form the Kikuchi bands on the phosphor screen. As θ is
small the intersection of the cones with the phosphor screen are straight lines.
One of the steps necessary to produce EBSD patterns in SEM is to tilt the
sample so that its surface makes an angle >60° with the horizontal. The main
effect of tilting is to reduce the path length of the electrons back scattered by
the lattice planes (62, 65). The Kikuchi bands form Kikuchi patterns from
which the orientation of the crystal will be defined. The phosphor screen is
observe by highly light-sensitive camera which transmits the acquired image
to a computer for further processing.
2.4.1 Automated evaluation of EBSD patterns
For the fully automated evaluation of the patterns, it is necessary that the
pattern (the position of bands and poles) are automatically detected by an al-
gorithm. Subsequently the pattern can be indexed and the crystallographic
orientation can be defined. Krieger Lassen et al (66) transformed the EBSD-
patterns using Hough transform. In this method (67) lines in the original im-
age are transformed into points, which are easier to be detected by algorithm.
The pattern quality does not affect the velocity of Hough transform, thus this
method is suitable for automated systems. During the Hough transform each
28
2. Background
Fig. 2.9: Scheme for formation of the Kikuchi bands from a point source
inside of the crystal (65).
point (xi, yi) is transformed into a sinusoidal curve in the Hough space, which
is characterized by ρ and ϕ according to the relation:
ρ(ϕ) = xicos(ϕ) + yisin(ϕ), ρ ∈ (0◦, 180◦), : ϕ ∈ (−R,R) (2.17)
each pixel belongs to infinite number of lines. A line in the Hough space is
defined by ρ and θ (ρ: the perpendicular distance of the line from the origin,
θ: the angle of the line) (fig. 2.10a). The sinusoidal curves corresponding to
each pixel on a line intersect at a point (ρ, θ) corresponding to the distance of
the line from origin and angle of the line (fig. 2.10b) (86). The whole image
can be transformed in this way into the Hough space.
For a given diffraction pattern several solutions (orientations) may satisfy the
diffraction bands detected by the image analysis routines. The solutions are
ranked by the software using a voting scheme. Confident index (CI) shows
how certain the correct orientation has been chosen between all possible ori-
entations. CI in the algorithm is given as
CI =(V1 − V2)
Videal(2.18)
29
2.4. General concepts of EBSD
Fig. 2.10: Schematic of Hough transform parameter. a)x-y space and b) ρ− θHough space (86).
where V1 and V2 are the number of votes for the first and second solutions
and Videal is the total possible number of votes from the detected bands. The
CI ranges form 0 to 1, a CI of 0 means V1 = V2.
2.4.2 Spatial and angular resolution
The spatial resolution is the minimum lateral distance between two different
orientations which can be separately indexed. The spatial resolution depends
on the material, beam accelerating voltage, specimen tilt and probe size and
the working distance. The atomic number also affects the spatial resolution.
Usually the effective spatial resolution is better than the physical resolution.
The area from which an EBSD pattern is acquired with an electron beam
focused on a 70◦ tilted sample is approximately elliptical (68). The major
axis is perpendicular to the tilt direction. A better resolution is obtained in
the direction parallel to the tilt axis. For characterizing the microstructures
with low angle boundaries the accuracy with which the relative orientation
between adjacent data points can be determined is of great importance. The
absolute orientation of a crystallite is with an accuracy of ∼ 0.5◦ − 1◦. The
angular resolution depends on calibration, sample alignment, Hough trans-
form and pattern acquisition parameter. The accelerating voltage of the probe
30
2. Background
current influences the angular resolution. According to Humphreys (68) with
increasing the the accelerating voltage the angular resolution improves. The
number of pixels in the CCD camera, the resolution of the digitized patterns
and accuracy of the pattern also affect the angular resolution.
2.5 Principle of the transmission electron micros-copy
The basic principle of transmission electron microscopy (TEM) is similar
to light microscopy (fig. 2.11). If a monochromatic electron beam enters
the crystal electron diffraction occurs. From the spot patterns obtained for a
single crystal, the lattice parameter and the orientation can be determined. If
the electron beam passes through a polycrystal, diffraction rings are obtained.
(14)
2.6 CuZrFig. 2.12 presents the phase diagram of the Cu-0.17wt%Zr alloy. The solu-
bility of Zr in Cu is very small, about 0.172wt% at a temperature of 972◦C.
Zr atoms are larger than Cu atoms. Due to this fact the Zr atoms are inertial in
Cu which leads to increase of strength of such alloys. Alloying Zr to Cu also
affects the temperature resistance of Cu. Generally the CuZr (with less than
0.172% Zr) alloys have high electrical conductivity, hardness, ductility and
also excellent resistance to softening at elevated temperatures. This material
is used for the applications, which acquire high strength and high electrical
and thermal conductivity.
31
2.6. CuZr
Fig. 2.11: Comparison of schematic of a) a light microscope and b) a trans-
mission electron microscope.
32
2. Background
Fig. 2.12: Phase diagramm of CuZr (69).
33
3
Experiments
3.1 Sample processing
3.1.1 Equal channel angular pressure deformation
The starting material was cut in to billets of 10mm × 10mm × 60mm and
subsequently processed by ECAP. The ECAP deformation was performed
at the institute of Werkstoffkunde und Werkstofftechnik TU Clausthal. The
deformation was performed at the room temperature with a press rate of
5mm/5min. The ECAP deformation was processed in a die with a die an-
gle of 90° using route BC. The billets were processed with 2 , 4 and 8
ECAP passes. The equivalent strain after 2, 4 and 8 ECAP passes is equal
to εeq ∼ 2.3, εeq ∼ 4.6 and εeq ∼ 9.2, respectively. The 3D EBSD measure-
ments were performed on the ED plane (fig. 3.1).
3.1.2 High pressure torsion deformation
The starting material was prepared in the form of small discs (fig. 3.2a
with diameter of ∼ 10 mm and thickness of ∼ 0.8 mm. The HPT was
35
3.1. Sample processing
Fig. 3.1: Sample reference frame in ECAP, TD (transverse direction), ND
(normal direction), ED (extrusion direction).
performed at the Erich Schmid Institute for materials science of Austrian
academy of science by the group of Professor Pippan. The samples were
subjected to HPT at room temperature under imposed pressure of 4.8 GPa
with a twisting rate of about 0.2/min. The sample reference frame is shown
in fig. 3.2a. In this project all the measurements were performed on the
radial-plane (fig. 3.2b. Separate samples were torsionally strained through
1/3, 2/3, 1 and 2 revolutions via HPT, which correspond to equivalent strains
of εeq ∼ 2.6, εeq ∼ 9.1, εeq ∼ 13.6andεeq ∼ 27.2 , respectively. The measure-
ments were taken at the position of 3mm from center of the disc. This position
is illustrated schematically in fig. 3.2b.
3.1.3 Annealing
Isochronous annealing of the samples were carried out in previous work by
X. Molodova to find out the temperature in which the microstructure showed
significant changes (70). This temperature was defined between 500°C and
700°C. The HPT samples were annealed at 525°C, 550°C, 575 °C and 600°C
in order to investigate the evolution of the microstructure, microtexture and
thermal stability of CuZr alloys processed by HPT. One of the ECAP samples
36
3. Experiments
Fig. 3.2: a) Sample reference frame in HPT, b) measurement plane and ge-
ometry of the sample.
after 8 ECAP passes were annealed at 650°C for 10 minutes to investigate the
grain boundary character distribution (GBCD).
3.2 Microstructure characterizationThe characterization of the microstructure was performed using high resolu-
tion scanning electron microscopy (SEM)/ electron back scatter diffraction
(EBSD) in 2-D and 3-D as well as transmission electron microscopy (TEM).
3.2.1 2D- EBSD- based orientation experiments
A Zeiss XB1560 crossbeam instrument was used for the characterization
of the microstructure, equipped with a Gemini-type field emission electron
gun, a Ga+ ion emitter (FIB), and secondary electron, back scatter electron
and scanning transmission electron detectors. For orientation microscopy an
EBSD detector (TSL/EDAX, Hikari S/N 1040 camera) was used. It is also
equipped with energy-dispersive X-ray spectroscopy (EDX) detector so that
37
3.2. Microstructure characterization
EBSD and EDX signals can be detected simultaneously.
3.2.2 3D- EBSD- based orientation experiments
The FIB column is positioned opposite to the EBSD camera (fig. 3.3), which
allows a precise and quick change of the sample from the FIB position (stage
tilt of 34◦) into the EBSD position (stage tilt of 0◦, sample tilt of 70◦). Be-
fore starting the EBSD measurement,the sample was fixed on a holder and the
holder was placed on pre-tilted stage (70◦) and inserted to the microscope. At
first the sample was aligned for EBSD analysis. Then the stage was tilted into
the FIB position (34◦). After identifying the SEM and FIB beam cross-over
point, the FIB position was saved. In order to find the precise position after
every new cycle a position marker (cross) was milled on the sample surface
close to the actual measurement area. This cross was detected at the begin-
ning of each new milling process. At this stage the milling filed was defined
(fig. 3.4). In order to prevent shadowing during the EBSD measurements
from the side walls of the measured area, the side walls were milled with a
current of 2 nA, so that the investigated area was bounded by 55◦ side walls.
The fine milling was performed using a beam current of 500 pA. After finish-
ing the settings of milling process, the sample was tilted into EBSD position
and the CCD camera was inserted into the chamber. Both, for FIB and EBSD
positioning, the marker as first detected at the beginning of each cycle. After
the software is once configured the milling and EBSD cycle runs fully auto-
matically until the predefined number of cycles has been reached. A cycle
is consisted of following steps: The EBSD camera is moved to the chamber,
the position marker is detected by image cross correlation and the sample is
brought to the reference position using beam shift, a reference image is taken
in the EBSD position, orientation mapping is carried out and subsequently the
EBSD camera is retracted, the stage moves to the milling position, the cross
marker is detected again by image cross correlation and using beam shift the
sample is brought to the reference position, the desired thickness is removed
from the surface of the sample and with that the milling process is finishes
38
3. Experiments
Fig. 3.3: Schematic of a dual beam system consisted of scanning electron
microscopy and focussed ion beam microscopy used for 3-D EBSD
measurements (71).
39
3.2. Microstructure characterization
Fig. 3.4: Schematic of a dual beam system consisted of scanning electron
microscopy and focussed ion beam microscopy used for 3-D EBSD
measurements.
and the stage is moved again to the EBSD position. In the system used here
for the 3D EBSD measurements the necessary steps for measurement process
are applied. The repositioning of the stage is accurate enough so that the re-
detection of the cross marker is possible, tilting of the stage is performed pre-
cisely, the drift of the stage is minimum and the position-correction algorithm
is precise enough to achieve the desirable resolution and the SEM and FIB
work stable over long measurement times (71). There are two measurements
strategies, namely grazing-incidence edge-milling (GIEM) method and the
low-incidence surface-milling (LISM) method. The schematic of both strate-
gies is illustrated in fig. 3.5. In the GIEM method the milling and EBSD is
performed under grazing incidence to one surface at the edge of the sample.
In the LISM the measurement will be performed on any volume close to the
sample surface. The disadvantages of this method is that the milling area
needs to be significantly larger than in the case of GIEM, in order to avoid
shadowing during EBSD measurement (71). In this study the GIEM method
is applied for the 3D measurements. There is another alternative setup for 3D-
EBSD measurements called rotation setup. In this method the EBSD camera
40
3. Experiments
Fig. 3.5: Schematic of a dual beam system consisted of scanning electron
microscopy and focussed ion beam microscopy used for 3-D EBSD
measurements (71).
is positioned below the FIB column. The sample will be moved from the
milling position to the EBSD position by rotating (72). It is conjectured that
the positioning of the stage in the rotation setup is more accurate than in tilt
set up. In tilt setup tilting of the stage up and down against gravity leads to
some inaccuracy for the tilt angle. The inaccuracy can be measured by cal-
culating the misorientation of the neighboring points in adjacent layers (71)
in a defect-free crystal. For the samples including defects, the inaccuracy of
the tilt angle is measured by averaging the misorientation of the neighboring
points, excluding those which exceed a certain threshold misorientation (71).
As described in ref. (71) the linear distorsion of the measurement is:
(l0 + δl)/l0 = sinα/ sin(α − δα) (3.1)
where l0 is the true length of the measurement area, and δl is the distortion
due to to misalignment. The correction of this distortion can be applied to the
final orientation map. In the instrument used in this study, the tilt inaccuracy
41
3.2. Microstructure characterization
is maximal 1◦ which leads to an inaccuracy of 100 nm on a orientation map
of 10μm at the very end of the measurement field.
3.2.3 Transmission electron microscopyTo get an insight to the microstructure of the highly deformed materials trans-
mission electron microscopy (TEM) analysis were carried out. The TEM
investigations were performed on a high resolution Jeol 2200FS at an accel-
erating voltage of 200kV . In order to get any information using TEM the
sample should be electron transparent which means it should be thin enough
to transmit sufficient electrons so that enough intensity will get on the screen.
In this project to prepare the samples for TEM investigation, the focussed ion
beam microscope (FIB) was used at an accelerating voltage of 30kV .
For the sample preparation using FIB, the area of interest with a width of
about 12μm and a thickness of 1.5μm is deposited by a protective layer of
platinum at an accelerating voltage of 30kV and a current of 93 pA using gas
injection system (GIS). Next step is milling large trenches on two sides of the
area of interest at maximum beam current. the sample is rotated from 52◦ to
7◦ and a cutout is performed so that the TEM-lamella is free from the down
part from the rest of the sample. In the next step the FIB mills trenches on
alternating sides of the membrane at a slightly lower current beam and the
sample thickness reduces from 4μm to 2μm. The fine milling will be contin-
ued on alternating sides of the membrane. The stage tilt to ensure the uniform
thickness of sample.
3.2.4 Hardness measurementsIn order to investigate the mechanical properties of the ultra fine-grained ma-
terials processed by severe plastic deformation methods hardness measure-
ments were carried out. Hardness defines the resistance of a metal to plastic
deformation (). There are different methods for measuring the hardness of the
sample, such as Martens-, Brinell, Rockwell, etc.. In this study the vickers
method was used. The load was 200 g and the exposure time was 10 sec. For
each strain 10 indentations were applied and the hardness was calculated by
42
3. Experiments
averaging of values which were calculated from each of the indentations.
HV =1.8544F
A≈ 0.1891F
d2(3.2)
where F is the force applied in newtons and d is the average length of the
diameter left by the indenter in mm.
43
4
Recrystallization behavior ofultra-fine grained Cu-Zralloy
In this chapter microstructure and microtexture evolution of the samples sub-
jected to different levels of strain via HPT in deformed and the subsequent
heat-treated state will be investigated. It will be discussed what is the physic
behind the behavior of the material subjected to high strains via high pressure
torsion under heat treatment with regard to grain growth and discontinuous
recrystallization.
45
4.1. Microstructure characterization
4.1 Microstructure characterization
4.1.1 Deformed state subjected to high pressure torsionExperiments
Fig. 4.1 shows the microstructure of the material before HPT deformation.
Cu-0.17wt%Zr alloy was produced using induction melting of highly pure
components at the Institute of Metallkunde and Metallphysik by the group of
Professor Gottstein. The material was subsequently homogenized at 950◦Cfor 10 hours. The grain size of the starting material before HPT deformation
was about 350μm. Fig. 4.1 shows the microstructure on two perpendicular
surfaces of the sample. It can be observed that the columnar grains which are
result of casting are present in the microstructure and on the other surface of
the sample the grains are more globular.
The samples were cut in the form of disks with a radius if 10mm and thick-
ness of 0.8mm and successively deformed via HPT under a pressure of 4.8
GPa at room temperature to 4 different revolutions, namely 1/3, 2/3, 1 and
2 corresponding to equivalent strains of 4.5, 9, 13.5 and 27, respectively at
radius of 3mm.
Results and Discussion
Mikrostructure Fig. 4.2 shows the inverse pole figure maps of the samples
after equivalent strains of 4.5, 9, 13.5 and 27. The color code shows the direc-
tions parallel to the measured plane (radial direction (RD)-plane). The areas
with different orientations are separated with grain boundaries. Desorienta-
tions between 2◦ and 5◦ are shown in red, between 5◦ and 15◦ in green and
desorientations larger than 15◦ in black. As the strain increases the original
grains and the new formed grains rotate and a fibrous microstructure devel-
ops. New grains are developed due to the induced high angle grain boundaries
and grain fragmentation.This fibrous microstructure becomes finer by further
increasing of strain as can be observed from fig. 4.2 and eventually from the
equivalent strain of 9 the saturation in refinement can be observed. Accord-
46
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
Fig. 4.1: Microstructure of the starting material (Cu-0.17wt%Zr) before HPT
deformation: a) normal plane, b) radial plane.
47
4.1. Microstructure characterization
ing to Pippan (31) the saturation of the refinement is affected by the temper-
ature, strain rate, strain path, alloying, crystal structure and pressure. The
microstructure exhibits a preferred direction at an angle to the axial direction,
which is according to Piappn (31) the typical feature of the HPT deformation
of the materials and was reported also by other authors (31).To have a better
understanding of the deformed microstructure after higher straining level, the
microstructure was studied using TEM. Fig. 4.3 shows the TEM-micrograph
of the deformed sample after a strain of 13.5.
In this microstructure it can be observed that partially fibrous microstructure
(blue arrays in fig. 4.3a and e) is existing neighboring the globular grains
(green arrays in fig. 4.3a, b and e). The microstructure also includes the de-
formation twinning as shown in fig. 4.3.
Fig. 4.4 shows the fraction of high angle grain boundaries (HAGB) with
a desorientation of larger than 15◦and low angle grain boundaries (LAGB)
with a desorientation smaller than 15◦. The amount of HAGBs increases to
about 80% with increasing strain and then reaches a steady state (Fig. 4.4).
After this stage the amount of HAGBs does not show significant changes with
increasing strain.
The same behavior could be recognized from the grain size evolution with
increasing strain (fig. 4.5).
Microhardness Fig. 4.6 represents the microhardness across the HPT sam-
ples, after application of pressure (4.8 GPa) and a torsional straining, so that
for 1/3 revolution there is a minimum of microhardness in the center of the
disc while at the outer edges of the disc the microhardness reaches a satu-
ration level at the vicinity of about 190 HV. With increasing the number of
revolutions and so the the imposed strain the microhardness in the center of
the disk increases apparently and for the samples subjected to 1 and 2 revo-
lutions, the microhardness is homogeneous across the diameter of the disk.
This is also reported by other authors (73, 74). Fig. 4.6b shows with increas-
48
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
Fig. 4.2: Inverse pole figure map of a Cu-0.17wt%Zr alloy subjected to high
pressure torsion at equivalent strains of a) 4.5, b) 9, c) 13.5, d) 27. The
color coding indicates the crystal directions parallel to radial direction.
49
4.1. Microstructure characterization
Fig. 4.3: TEM image of the microstructure of Cu-0.17wt%Zr subjected to a
strain of 13.5 via high pressure torsion in different magnifications.
50
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
Fig. 4.4: Evolution of high angle and low angle grain boundaries at different
strain subjected by high pressure torsion in Cu-0.17wt%Zr samples.
Fig. 4.5: Grain size evolution at different strain levels subjected by high pres-
sure torsion in Cu-0.17wt%Zr samples.
51
4.1. Microstructure characterization
ing the strain level microhardness increases at first and then from strain of
about 9 a steady state appears to be reached. After a strain of 27 the material
reveals a hardness of approximately 192 HV .
Microtexture Montheillet et al. (75) identified the ideal orientations dur-
ing torsion experimentally which are presented in table2.2. According to the
geometry of the torsion test these components are either centrosymmetric
, namely A∗1, A∗2,C or are present in the form of a twin symmetry, namely
A/A, B/B (75). In most of the components the <uvw> orientations is close to
the close-packed direction of the fcc structure (< 110 >-direction). The ones
which do not show this property are marked with a superscript star (A∗1, A∗2).
Figs. 4.7, 4.8, 4.9, 4.10 show the orientation distribution function using the
ϕ2 =constant (0◦ − 90◦) in steps of of 15◦ of the samples at different levels
of shear strain, ε ∼ 4.5, 9, 13.5, 27, respectively. The sample symmetry is not
imposed for calculation of the ODFs, thus ϕ1 ranges from 0◦ to 90◦. The tex-
ture is characterized by components aligned along three f1, f2 and f3 fibers
for the sample at a strain of 4.5. The f1 fiber starts at A∗1 and passes through
A/A and ends at A∗2. The f1 fiber includes the {111} partial fiber, with the
orientation density being strong at A∗2 side. The A∗1 is missing along the f1fiber. The f2 fiber starts at C and passes through B/B and AA and ends at A∗1.
Thus the f2 fiber consists of C−B/B−A/A < 110 > partial fiber and A/A−A∗1{111} partial fiber meeting at the common A/A position. Along f3 fiber ( f2)
the C component ({100} < 011 >) has the highest orientation density. The f3fiber which is symmetric to f2 includes the A/A − B/B − C < 110 > partial
fiber and A∗2 − A/A {111} partial fiber. The maximum orientation density is
at C. The maximum texture intensity at the shear strain of 4.5 is 11.2 at the
(90◦ 40◦ 0◦) with a 5◦ shift along φ (rotation of 5◦ around tangential direction)
from the C component.
With increasing shear strain to 9 along the f1 the A∗1 component is absent as
for the shear strain of 4.5 (fig. 4.8). Fig. 4.8 shows that along the f1 fiber
the maximum orientation density is between A and A∗2 is distributed more
uniform. The highest orientation density is around the A component which
could be developed by rotating the A∗2 30◦ around {111} (ND-direction).
52
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
Fig. 4.6: Microhardness evolution: a) across the HPT deformed samples (Cu-
0.17wt%Zr) subjected to different number of revolutions, b) of HPT
deformed samples (Cu-0.17wt%Zr) subjected to different strain levels.
53
4.1. Microstructure characterization
The C component is not a stable orientation (45), thus is rotated 34◦ or 55◦around < 101 > and the B and the A components, respectively, become the
strongest components along the f2 fiber. The same for the f3 fiber the A∗2 ro-
tates around < 101 > to A and B components. The highest texture intensity at
the shear strain of 9 is 5.1 at the (175◦45◦50◦) orientation.
At strain of 13.5 along the f1 fiber the A∗1 is absent and the highest orien-
tation density is around the A component as before fig. 4.9. Along the f2and f3 fibers the C component becomes weaker, due to the instability of this
component and develops by rotating 36◦ around the < 101 > direction (TD-
direction) to the B component which got stronger compared to the strain of 9.
The highest texture intensity is 5.9 at an orientation of (295◦50◦50◦).At strain of 27.2 the distribution of texture components along the three f1, f2and f3 is nearly the same as ODFs of the shear strain of 13.5 (fig. 4.10). The
A∗1 component is hardly ever developed during the HPT deformation of the
Cu-0.17wt%Zr. The highest orientation density at this level of shear strain
is around the A and B. The maximum texture intensity is about 5.7. The
main result of the texture analysis during HPT deformation is that textures
developed show concentrations around the f1, f2 and f3 fibers which consist
of {111} and < 110 > partial fibers. In position and the strength of the main
texture components, texture evolution seems to stabilize after shear strain of
9. With increasing the shear strain the microstructure becomes homogeneous
and reaches steady state as discussed in the microhardness and grain size evo-
lution.
4.1.2 Annealed state after subjection to high pressure tor-sion
Experiments
The samples subjected to HPT were annealed isothermally afterwards at dif-
ferent temperatures. In this part the results of the annealing at 550◦ C of the
54
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
Fig. 4.7: Constant ODF sections (ϕ2 = 0◦, 15◦, 30◦, 45◦, 60◦, 75◦, 90◦) of ori-
entation distribution functions of the deformed sample at a shear strain
of 4.5
55
4.1. Microstructure characterization
Fig. 4.8: Constant ODF sections (ϕ2 = 0◦, 15◦, 30◦, 45◦, 60◦, 75◦, 90◦) of ori-
entation distribution functions of the deformed sample at a shear strain
of 9.
56
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
Fig. 4.9: Constant ODF sections (ϕ2 = 0◦, 15, 30◦, 45◦, 60◦, 75◦, 90◦) of ori-
entation distribution functions of the deformed sample at a shear strain
of 13.5.
57
4.1. Microstructure characterization
Fig. 4.10: Constant ODF sections (ϕ2 = 0◦, 15◦, 30◦, 45◦, 60◦, 75◦, 90◦) of
orientation distribution functions of the deformed sample at a shear
strain of 27.
58
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
strained samples to 4.5 and 13.5 will be analyzed.
4.1.3 Results and Discussion
Microstructure In this part the microstructure evolution of the sample sub-
jected to strains of 4.5 and 13.5 will be analyzed. Independent of the strain
level subjected by HPT, it can be observed that during annealing of the sam-
ples new defect-free areas appear. The fraction of these areas increased with
increasing annealing time (figs. 4.11, 4.12). With increasing the level of
strain these areas (discontinuities) developed slower. Fig. 4.11 depicts the
evolution of the microstructure during isothermal annealing at 550°C of the
samples subjected to HPT to shear strain of 4.5. From the inverse pole figures
we can observe that after 60 seconds there are some discontinuities devel-
oping in the microstructure. Fig. 4.12 shows the microstructure evolution
of the sample subjected to an equivalent strain of 13.5 during isothermal an-
nealing at the same temperature of 550◦C. The discontinuities at this level of
strain appeared after 600 seconds. The average grain size of the annealed mi-
crostructure with increasing the equivalent strain level after 1800 seconds of
annealing at 550◦C decreased from 1.31μm to 0.69μm (4.13). The evolution
of the grain size during annealing at 550◦ C is shown in fig. 4.13. At the very
early stages of annealing (up to about 60 seconds) in both microstructures the
grain size increased (the stage marked with I in fig. 4.13) which is because
of grain coarsening. It means that the existing grains with high angle grain
boundaries developed during deformation start to grow slightly and develop
a microstructure with more equiaxed grains. With increasing annealing time
(from 60 seconds to 600 seconds)grain size does not show significant changes
(marked with II in fig. 4.13). This could be provoked by pinning effect of the
dispersions on the grain boundaries and hinting growth of the grains. Accord-
ing to the equation (4.1) ((14)):
d >d
1 − ddmax
(4.1)
59
4.1. Microstructure characterization
where d is the average grains size of the pinned grain structure and dmax is the
maximum grain size according to equation (4.2)((14)):
dmax =2
3
1
α
dp
f(4.2)
where dmax is the maximum grain size (grain sizes calculated from this equa-
tion are normally larger than in reality) which is pinned by the particles of the
size dp, α is a constant relating radius of curvature of grain boundaries and
grain size, dp is the size of the particles and f is the fraction of the particles in
the microstructure. At the equivalent strain of 13.5 and the volume fraction of
the particles, calculated from the lever rule, is about 0.61% . The maximum
grain size (from equation (4.2)) which can be pinned by the particles of the
size about 10nm is about 2μm. These particles formed during annealing of the
samples. The TEM pictures of the samples in the deformed state and early
stages of annealing show (fig. 4.14) there are some coffee bean effects which
are the result of formation of the precipitates in the microstructure. It could
be observed that after annealing the fraction of these coffee beans increased
. When the volume defects in the microstructure are small, around these de-
fects a strain-field forms. Lattice-strain effects around the precipitates appear
like butterflies or coffee beans in the image (76)(fig. 4.14). With annealing
of the sample after 60 seconds, the size of small precipitates increased and
reached the size of 10 nm. The reason of formation of the precipitates in the
microstructure is the saturation of the microstructure with Zr. As it can be ob-
served in fig. 2.12 the solubility of Zr in Cu is 0.178wt% in Cu at 950◦C. The
starting material was homogenized at 950◦C for 10 hours and then quenched
to the room temperature. and so the Zr atoms stay in solid solution in Cu-
matrix but the matrix is saturated. At 550◦C Zr atoms come out of the matrix
and form the precipitated of the form Cu9Zr2. The critical grain size for a
grain to grow discontinuously in the microstructure from equation (4.1) will
be about 380 nm. In both microstructures the average grain size up to an-
nealing time of 600s is under 380 nm and so most of the grains where pinned
with the precipitates. Due to this the grain size at this stage did not show
significant changes. According to Oscarsson et al. (77) and Humphreys et
al. (61) the transition from discontinuous to continuous recrystallization oc-
60
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
curs when the HAGB% in the deformed structure increases to about 60-70%.
Under conditions at which continuous recrystallization occurs, the amount of
HAGBs does not show significant changes even at temperatures at which re-
crystallization would occur (78). Fig. 4.15 shows the evolution of HAGBs
during annealing of the Cu-0.17wt%Zr samples at different strain levels. It
depicts that the fraction of HAGBs in the deformed structure is over 60% and
during annealing does not show significant changes which could be a clue of
continuous recrystallization.
Microhardness During annealing the changes in the microstructure due to
recovery or recrystallization affect the mechanical properties of the sample,
namely the hardness of the material. Fig. 4.16 shows microhardness evolution
of Cu-0.17wt%Zr samples subjected to equivalent strains of 4.5 and 13.5 and
subsequent isothermal annealing. The material shows slight hardening at very
early stages of annealing. The increase of hardness could be due to formation
of precipitates and the strain field around them at early stages of annealing.
With increasing the annealing temperature the softening processes are faster
and hence hardness decreases faster. The hardness plateau increases with
increasing strain.
Stored energy in the microstructure During deformation of the metals,
the deformation energy stores in form of lattice defects. The deformation his-
tory and also the crystal orientation affect the stored energy in the microstruc-
ture (79, 80). There are different approaches for calculating the stored energy
in the microstructure, namely the X-ray or neutron diffraction peak broad-
ening measurements (79, 81), diffraction pattern quality in SEM and TEM
measurements by using the Read-Shockley equation for measuring the en-
ergy stored in small angle grain boundaries as an indirect measure of dislo-
61
4.1. Microstructure characterization
Fig. 4.11: Microstructure evolution of Cu-0.17wt%Zr subjected to a shear
strain of 4.5 via HPT and subsequent annealing at 550◦ C for a)10s, b)
30s, c) 60s, d) 300s, e) 600s and f) 1800s.
62
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
Fig. 4.12: Microstructure evolution of Cu-0.17wt%Zr subjected to a shear
strain of 13.5 via HPT and subsequent annealing at 550◦ C for a) 10s,
b) 30s, c) 60s, d) 600s, e) 1800s and f)3600s.
63
4.1. Microstructure characterization
Fig. 4.13: Average grain size of Cu-0.17wt%Zr samples, calculated from
EBSD data, subjected to strains of 4.5 and 13.5 and a subsequent an-
nealing at 550°.
64
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
Fig. 4.14: TEM micrographs of the sample subjected to a strain of 13.5 and
successive annealing at 550◦ in which coffee bean effect demonstrates
the formation of new nano-particle during heat treatment.
65
4.1. Microstructure characterization
Fig. 4.15: High angle grain boundary evolution of the Cu-0.17wt%Zr sam-
ples subjected to different levels of equivalent strain by high pressure
torsion during isothermal annealing at 550◦C.
66
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
Fig. 4.16: Evolution of microhardness of Cu-0.17wt%Zr samples at strain
levels of a) 4.5 and b) 13.5 subjected by high pressure torsion.
67
4.1. Microstructure characterization
cation density (82, 83), interpretation of lattice rotations in terms of GNDs in
EBSD measurements based on the kernel average misorientation (KAM) cal-
culations (84, 85). In this project the KAM value is used as an estimation of
the stored energy in the microstructure. KAM value in EBSD meaurements
is calculated by averaging the misorientation of each point in the center of
kernel and the nth neighbor pixels (86):
KAMn =1
6n
∑θi (4.3)
Misorientations larger than θmax is not included in the calculations. For this
study the θmax is 5◦. The density of geometrically necessary dislocations to
create the lattice curvature can be calculated as following (87, 88, 89, 90):
ρGND =ω
b(4.4)
where ω is the lattice curvature and b is the Burgers vector. The average
value of calculated kernel average misorientation for every microstructure
can be placed in the equation (4.4) for the lattice curvature.The energy from
dislocations can be calculated from the following equation:
E =1
2ρGb2 (4.5)
For calculation of the ρGND from EBSD measurements the following equation
(4.6) was used (90):
ρGND =2πθKAM
180 × b × n × a(4.6)
where θKAM is the local misorientation calculated from EBSD measurements,
b is the Burgers vector, n is the number of neighbor for calculating the local
misorientation and a is the step size used for performing of the EBSD mea-
surements.
Equations (4.3) and (4.4) depict that there is a linear relationship between
the geometrically necessary dislocation density and the kernel average mis-
orientation value, so that the kernel average misorientation can be used to
68
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
evaluate the stored energy for every given point in the EBSD measurement.
The higher the kernel average misorientation of each point, the larger the
density of geometrically necessary dislocations and the stored energy in that
point. The kernel average misorientation maps presented in figs. 4.17, 4.18
and 4.19 are showing that with increasing annealing time, the stored energy
from geometrically necessary dislocation (GND) decreases. It shows that the
recovery process is running parallel to grain coarsening, considering the grain
size evolution during annealing, at early stages of annealing. There are some
areas in figs. 4.17e and 4.18d, which lessen their stored energy faster than
others. These grains grow in the still deformed areas with higher densities
of dislocations and discontinuities develop at this stage. It can be observed
that the discontinuities develop faster at lower strain levels. The cause of that
could be referred to both higher dislocation densities and higher amounts of
high angle grain boundaries at larger strain levels.The driving force for devel-
oping such discontinuities could be, as mentioned, the stored energy caused
by defect structure (dislocations) or it could be driven by boundary curvature.
For a grain size of about d = 0.2 μm and average grain boundary energy of
0.5 Jm2 the driving force is pGB ≈ 7.5 , which is in a comparable magnitude to
the dislocation energy from equation (4.5), which is approximately 12.5 MPawith dislocation density of about ρ ≈ 1015m−2. Since the driving force for
both processes, namely discontinuous recrystallization or primary recrystal-
lization and discontinuous grain growth, is comparable, the character of the
microstructure evolution during annealing of severely deformed microstruc-
ture subjected to HPT should be analyzed by considering other parameters.
Microtexture The texture evolution during annealing of the samples sub-
jected to strain of 4.5 and 13.5 (figs. 4.20 and 4.21) show that the texture
components developed during the HPT deformation exist after annealing at
550◦C. The position of texture components changes during annealing of the
samples strained to 4.5 mostly along the φ (around the radial direction), while
the position of the texture components for the sample subjected to a strain of
69
4.1. Microstructure characterization
Fig. 4.17: Kernel average misorientation maps (3rd neighbor) of the Cu-
0.17wt%Zr subjected to strain of 13.5 during annealing at 550◦ after
a) 10s, b) 30s, c) 60s, d) 300s, e) 600s and f) 1800s.
70
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
Fig. 4.18: Kernel average misorientation maps (3rd neighbor) of the Cu-
0.17wt%Zr subjected to strain of 13.5 during annealing at 550◦ after
a) 10s, b) 30s, c) 60s, d) 600s, e) 1800s and f) 3600s.71
4.1. Microstructure characterization
Fig. 4.19: evolution of overall density of geometrically necessary dislocations
in the Cu-0.17wt%Zr samples subjected to equivalent strains of 4.5 and
13.5 during isothermal annealing at 550◦C.
72
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
13.5 does not change during annealing up to 300 seconds. The shift of the
texture components could be referred the discontinuities developed and also
orientation pinning during annealing of the samples. Since the discontinuities
develop slower in sample subjected to a strain of 13.5, the shift of the texture
components starts not before longer annealing times. The maximum texture
intensity increases during annealing (figs. 4.20 and 4.21). The strongest tex-
ture components are the B and B with increasing the annealing time for both
strain levels, although the strongest starting texture component was different
for both of them. After 600 seconds of annealing at 550◦C the fraction of
these both components increases significantly. The increase of texture in-
tensity and dominated texture component could be referred to both primary
recrystallization and also grain growth. In the case of primary recrystalliza-
tion the nucleation is preferably dominated by a specific texture component,
i.e. here the B and B components. To investigate the correlation between
the stored energy in each texture component and fraction of texture compo-
nents, the evolution of the geometrically necessary dislocation density in each
texture component during annealing was calculated from the kernel average
misorientation values (fig. 4.22). The analysis of the evolution of ρGND as
shown in fig. 4.22 revealed that in different shear texture components the dis-
location density and the stored energy of the dislocations are almost identical.
Therefore the highest fraction of B and B components is not related to their
stored energy and is probably caused by the character of grain boundaries
which may be referred to the discontinuous grain growth.
Fig. 4.23 presents the correlation of the grains size and the related stored en-
ergy.The microstructure is partitioned in different grain sizes and the stored
energy of each of the partitions was calculated. This figure shows that the
growing grains in the micostructure decrease their stored energy faster. It
could be realized from this figue that the driving force for the discontinuously
growing grains in the microstrucutre is obtained from the energy of disloca-
tions.
73
4.1. Microstructure characterization
Fig. 4.20: Orientation distribution of the Cu-0.17wt%Zr subjected to an
equivalent strain of 4.5 during annealing at 550◦ after a) 10s, b) 30s,
c) 60s, d) 300s, e) 600s, f) 1800s and g) 3600s.
74
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
Fig. 4.21: Orientation distribution of the Cu-0.17wt%Zr subjected to an
equivalent strain of 13.5 during annealing at 550◦ after a) 10s, b) 30s,
c) 60s, d) 300s, e) 600s, f) 1800s and g) 3600s.
75
4.1. Microstructure characterization
Fig. 4.22: Evolution of density of geometrically necessary dislocations in
shear texture component in the Cu-0.17wt%Zr subjected to an equiva-
lent strain of 13.5 during annealing at 550◦C.
76
4. Recrystallization behavior of ultra-fine grained Cu-Zr alloy
Fig. 4.23: Relation of the kernel average misorientation evolution with grain
size in deformed microstructure subjected to a strain of 13.5 in de-
formed and in annealed state.
77
4.2. Conclusion
4.2 ConclusionIn this part of the project the microstructure and microtexture of the materials
subjected to HPT at two different levels of strain (ε ∼ 4.5and13.5) were ana-
lyzed. The microstructure evolution of the heat-treated samples showed that
there were some grains, growing discontinuously during heat treatment of the
samples. Due to the high fraction of high angle grain boundaries, it was ex-
pected that the material shows homogenous changes of microstructure during
heat treating, which was not the case. Accordingly the stored energy evo-
lution depicted that the stored energy decreases during annealing processes.
The texture results demonstrated the dominance of the B component and Bcomponents in the annealed state. The stored energy of each texture com-
ponent existing in the deformed microstructure was approximated using the
kernel average misorientation, however there was no correlation between the
stored energy of the texture components and their appearance during heat
treatment. A correlation between the grain size and the stored energy was ob-
served. During annealing of the samples the larger grains showed the smallest
KAM-value. It could be explained by the fact that grains reducing their stored
energy grow in the deformed microstrcture and develop a bimodal structure.
The driving force for formation of these grains was obtained most probably
from the stored energy of the dislocations. This can be an indication of pri-
mary recrystallization. But the preferable domination of specific texture com-
ponents was not related to their stored energy but is probably caused by the
character of grain boundaries. Since the driving force for the discontinuous
grain growth and primary recrystallization is in the same order of magnitude,
it can be concluded that both processes are active during heat treatment of the
strongly strained samples.
78
5
3-D Microstructure
5.1 3-D based microstructure and microtexturecharacterization
In this chapter in order to analyze the 3-D microstructure from the 3-D EBSD
data set, the EDAX-TSL OIM analysis software package was used. All 2-D
data sets were cleaned using the CI standardization algorithm. For 3-D EBSD
analysis it is of great importance to properly align the layers before recon-
structing the microstructure. In this work the alignment was performed using
a code developed at Carnegie melon university (CMU) by the group of Prof.
Rollett and Prof. Rohrer. For the first alignment step the approach is based on
minimizing the disorientation between corresponding voxels in adjacent lay-
ers (91). The secondary alignment performs a rigid shift to the coordinates of
the third layer, so that the average triple line direction is perpendicular to the
surface (13, 92).
79
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.1: Microstructure of the starting material (Cu-0.17wt%Zr) before
ECAP deformation (70).
5.1.1 Deformed state subjected to equal channel angularpressing
Experiments
Fig. 5.1 shows the microstructure of the material before ECAP deformation.
Cu-0.17wt%Zr alloy was produced using induction melting of highly pure
components at the Institute of Metallkunde and Metallphysik by the group of
Professor Gottstein. The material was subsequently homogenized at 940◦ C
for 12 hours. The homogenized as received material was deformed by one
ECAP pass, and subsequently annealed at 650◦C for 1 hour in order to obtain
a homogeneous, fully recrystallized, fine structure with an average grain size
of 6μm. Billets with 10mm× 10mm cross section and 60mm length were then
processed by ECAP at room temperature using 2, 4 and 8 passes via route
BC , as described in chapter experimental methods. Afterwards workpieces of
10mm × 4mm × 1mm (after 2 and 8 ECAP passes), and 6mm × 5mm × 1mm(after 8 ECAP passes) were cut by spark erosion. Two cross sections of the
sample were mechanically ground and polished so that a sharp rectangular
80
5. 3-D Microstructure
corner of two cross sections were prepared. In the final step of preparation
the silica suspension at 250 nm coronation was used.
The preparation should be performed in a way that the common edge between
two surfaces is sharp. 3-D EBSD was conducted as described in chapter Ex-
periments in a dual-beam Zeiss XB1560 microscope. 3-D EBSD proceeds by
fully automated serial sectioning via FIB and the subsequent high resolution
EBSD measurements on each of the exposed layers (93, 94, 71, 90). For the
3-D EBSD measurements the sample were mounted on a sample holder and
placed on a pre-tilted stage (70◦). The details of the 3-D EBSD approach
were delineated in chapter Experimental methods. The FIB was operated at
an accelerating voltage of 30 kV and a 2 nA and 500 pA beam for coarse- and
fine milling, respectively. The EBSD measurements were performed at an
accelerating voltage of 15 kV .
Results and Discussion
Microstructure Figs. 5.2, 5.3, 5.4 show the tomographic reconstruction of
the microstructure of the samples after 2, 4 and 8 ECAP passes, respectively.
The EBSD measurements were performed on the extrusion plane (ED); this
means the plane normal direction was the extrusion direction (ECAP direc-
tion). The inverse pole figure colors indicate the miller indices of different
directions parallel to the ED plane. The EBSD measurement was performed
with more than 90% correctly indexed points at a confidence index value of
above 0.1 before cleaning up for the 2-pass ECAP sample and over 80% for
the 4-pass and 8-pass ECAP samples. The decrease of the indexing grade with
increasing number of passes result from the increasing of the defect density
inherited by ECAP. Elongated grains can be seen on all three microstructures
within the transverse direction (TD) plane. The amount of elongated grains
decreases explicitly with increasing the ECAP pass number. In order to make
sure that the elongated grain shapes especially in 8-passed ECAP sample are
not caused by incorrect alignment, corresponding 2-D EBSD measurements
81
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.2: Tomographic microstructure of Cu-0.17wt%Zr after 2 ECAP passes,
reconstructed from two dimensional EBSD measurements using Par-
aview software. The color code indicates the crystal direction parallel
to the ECAP direction (ED).
82
5. 3-D Microstructure
Fig. 5.3: Tomographic microstructure of Cu-0.17wt%Zr after 4 ECAP passes,
reconstructed from two dimensional EBSD measurements using Par-
aview software. The color code indicates the crystal direction parallel
to the ECAP direction (ED).
83
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.4: Tomographic microstructure of Cu-0.17wt%Zr after 8 ECAP passes,
reconstructed from two dimensional EBSD measurements using Par-
aview software. The color code indicates the crystal direction parallel
to the ECAP direction (ED).
84
5. 3-D Microstructure
Fig. 5.5: Microstructure of Cu-0.17wt%Zr after 8 ECAP passes (route BC) in
two dimensions.
were additionally carried out within the TD plane of the 8-pass ECAP sam-
ple. The 2-D inverse pole figure map of this measurement is shown in 5.5.
It confirms that the grain shapes obtained from TD sections in 3-D recon-
struction are correct. Elongated grains in ECAP samples were already re-
ported by other authors (95, 96, 97, 98, 99). The elongated grains in ECAP
are achieved through simple shear deformation on the intersection plane of
the two ECAP channels which has an angle of 45◦ to the extrusion direction
(ED). The elongated grains are the result of the shearing within shear plane.
In order to investigate the gradual deformation-simulated formation of high
angle grain boundaries in the current 3-D case the amount of high angle grain
boundaries (misorientation above 15◦) and low angle grain boundaries (mis-
orientation between 2◦ and 15◦) for all three microstructures was analyzed.
For this purpose the length of all grain boundaries in the 3-D microstruc-
ture was calculated. The same calculation was made for the low angle grain
boundaries. Fig. 5.6 shows that with increasing number of ECAP passes the
fraction of high angle grain boundaries increases from about 25% (2-pass)
85
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.6: Evolution of grain boundary fraction after 2, 4 and 8 ECAP passes
calculated from the 3-D EBSD data sets.
to 65% (8-pass). One of the most important features of ECAP processing
is that the material can undergo very high strains by repetitive pressing ow-
ing to the cross-section preserving strain path (100). In this procedure the
sub-grain boundaries tend to gradually form into high angle grain boundaries
through accumulation and absorption of dislocations (35). This procedure
produces ultra-fine grains that are separated by high angle boundaries. ECAP
processing route BC is the most effective route for producing ultra fine grains
(35, 36, 32).
Crystallographic texture development Conventionally, orientation distri-
bution function (ODF) determination is conducted by measurement of several
XRD (X-ray diffraction) pole figures. These calculations can lead to series
expansion inaccuracies (in case of Fourier Expansions) or under-determined
equation systems (in case of direct inversion) which can be avoided when a
microtexture technique such as 2-D EBSD is used to obtain the orientation
86
5. 3-D Microstructure
distribution. While both XRD and 2-D EBSD are surface-sensitive meth-
ods, in the 3-D EBSD technique we sequentially removed layers of 50nm and
100nm thickness and hence obtained a volume Ðintegrated measure of the ori-
entation distribution. This is of great importance for studying the texture with
respect to orientation gradients or inhomogenities resulting from incomplete
grain refinement in ECAP materials. Also with this method the tomographic
aspect of the texture components can be analyzed in the microstructure. Ori-
entation distribution function of the sample after 2, 4 and 8 ECAP passes were
calculated from the 3-D EBSD data set using the harmonic series expansion
method. Wright et al (101) suggested that approximately 10,000 grains pro-
duce a good sampling in rolled steel and threaded steel rods for obtaining a
statistically robust ODF. In this study the number of grains in the 3-D EBSD
data set is 5962 in case of 2-ECAP, 11458 and 12007 for the 4-ECAP and
8-ECAP samples, respectively. Fig. 5.7 shows the ODFs of three samples,
namely, 2-, 4- and 8-pass ECAP as obtained from 3-D EBSD data. In fig.
5.7 only the ϕ2 = 45◦ sections are presented. The red markers in fig. 5.7
indicate the locations of the ideal shear texture components of FCC material
in the ECAP reference system. Molodova et al calculated the ODFs of the
Cu-0.17wt%Zr after 2, 4 and 8 ECAP passes using XRD measurements (7)
(fig. 5.8). The comparison of the ODFs obtained from the 3-D EBSD data
sets with those obtained by XRD reveals some deviations which we attribute
to the fact that the ECAP process does not lead to a homogeneous deforma-
tion but to texture gradients through the thickness. While the 3-D EBSD data
provide a through-thickness integration of the texture, the XRD data are sur-
face sensitive.
The occurrence of texture gradients is documented in fig. 5.9 which provides
the ODFs of three different through thickness slices for samples after 4 ECAP
passes and after 8 ECAP passes. The chosen ODFs in three different slices
for each sample demonstrate that the samples are characterized by texture
gradients both with respect to the position and orientation density of the tex-
ture components. For the 4-pass ECAP sample the strongest component is
an orientation between BE and CE at a distance of 1 μm from the surface.
At 4 μm from the surface an orientation between BE and A∗2E appears as the
87
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.7: Orientation distribution functions of the deformed samples in the
measured volume obtained from the 3-D EBSD data a) after 2 ECAP
passes b) after 4 ECAP passes and c) after 8 ECAP passes (route BC).
The red dots indicate the locations of the ideal shear texture compo-
nents in the ECAP reference system, after a 45◦ rotation.
88
5. 3-D Microstructure
strongest component in this specimen. At 7.5 μm from the surface again an
orientation between BE and CE has the highest orientation density. In the
8-pass ECAP sample the texture gradients between the different slices are
much weaker than in the 4-pass ECAP sample, i.e. the texture becomes more
homogeneous as the number of ECAP passes increases. In the 8-pass ECAP
sample an orientation between BE and A∗2E is the strongest texture component
with an almost constant orientation density.
As shown in fig. 5.10 the texture after 2 ECAP passes is characterized by
orientation concentration on three fibers, designated as f1, f2 and f3 (98).
The ODF sections show that the monoclinic symmetry is not present along
these fibers, namely there is a large difference between the orientation den-
sities of the AE and AE , and also BE and BE . The f1 fiber begins with the
A∗1E and passes through the AE/AE position ending at the A∗2E orientation.
Thus the f1 fiber consisting of the A partial fiber ({111}-plane || shear plane)
is much denser on the AE orientation. In this figure the A∗2E component is
strongly shifted from its ideal position about 9◦ along ϕ1 (around TD) and
about 20◦ along ϕ (around ED). The f2 fiber starts at CE orientation an passes
through BE/BE and AE/AE , ending at A∗1E . Hence the f2 fiber consists of
both A-partial fiber ({111}-plane ‖ shear plane) and the B-partial fiber (〈111〉-direction ‖ shear direction) which meet at AE/AE position. Finally the f3 fiber
contains both A- and B-partial fibers. The maximum orientation intensity oc-
curs close to the AE orientation. The AE/A component is not present in the
deformed microstructure after 2 ECAP passes. The second strong component
present on the ODF is the CE component. The main texture components after
4 ECAP passes are also distributed along the f1, f2 and f3 fibers. Along the
f1 fiber the A∗1E component is strong. Fig. 5.11 depicts that most of the shear
texture components are present along the f1, f2 and f3 fibers. It shows that
the f1 fiber is reasonably complete across A∗1E −AE −A∗2Eand A∗1E −AE −A∗2E .
Fig. 5.11 also represents a complete f2 fiber (across CE − BE − AE − A∗1E)
and f3 fiber across (A∗2E − BE − AE − CE). The ODF sections for the sample
89
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.8: Orientation distribution functions of the deformed samples a) after
2 ECAP passes b) after 4 ECAP passes and c) after 8 ECAP passes
(route BC) obtained from XRD measurements and subsequent series
expansion calculations (7). The red dots indicate the locations of the
ideal shear texture components in the ECAP reference system, after a
45◦ rotation.
90
5. 3-D Microstructure
Fig. 5.9: ϕ2 = 45◦ section of orientation distribution function of different
slices from 3-D EBSD measurements after 4 ECAP passes: a)1 μm,
b)4 μm, c) 7.5 μm from the surface. ϕ2 = 45◦ section of orientation
distribution function of different slices from 3-D EBSD measurements
after 8 ECAP passes: d) 1 μm , e) 4 μm and f) 7.5 μm from the surface.
after 8 ECAP (fig. 5.12 passes depict also the ideal shear texture compo-
nents are present along f1, f2 and f3 fibers. The f1 fiber is complete across
the A∗1E − AE − A∗2E and less complete across A∗1E − AE − A∗2E as a result of
orientation distributions concentrated around the A∗1E and A∗2E components
and underdevelopment of AE component. The f2 and f3 fibers are also not
complete as the orientation distribution is concentrated at A∗1E and A∗2E com-
ponents and AE , BE components are underdeveloped. The strongest texture
components are A∗1Eand A∗2E orientations. Comparing the ODFs of the sample
after 4 and 8 ECAP passes, the strongest components after 8 ECAP passes
are similar to those after 4 ECAP passes. There are difference evident be-
tween these two deformation paths. ODF data that derived from 3-D EBSD
data sets shows deviations from the ideal shear texture components. Such
deviations between ideal shear texture components and experimental ECAP
textures were observed before (7). They were attributed to the geometry of
91
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.10: Constant ODF sections (ϕ2 = 0◦, 15◦, 30◦, 45◦, 60◦, 75◦, 90◦) of
orientation distribution functions of the deformed sample in the mea-
sured volume obtained from the 3-D EBSD data after 2 ECAP passes.
92
5. 3-D Microstructure
Fig. 5.11: Constant ODF sections (ϕ2 = 0◦, 15◦, 30◦, 45◦, 60◦, 75◦, 90◦) of
orientation distribution functions of the deformed sample in the mea-
sured volume obtained from the 3-D EBSD data after 4 ECAP passes.
93
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.12: Constant ODF sections (ϕ2 = 0◦, 15◦, 30◦, 45◦, 60◦, 75◦, 90◦) of
orientation distribution functions of the deformed sample in the mea-
sured volume obtained from the 3-D EBSD data after 8 ECAP passes.
94
5. 3-D Microstructure
the deformation process, strain hardening, through thickness gradients, and
friction conditions. As fig. 5.13 depicts the volume fraction of the other tex-
ture components has decreased after 8 ECAP passes. This can be referred to
the fact that in route BC a shear reversal occurs, i.e. the third pass imposes
the reverse shear relative to the first pass and this strain path change is re-
peated every four passes. The weakening of the texture is due to the strain
path. This leads to weakening of the texture intensity with increasing the pass
number.Fig. 5.13 depicts the fraction of shear texture components developed
during the ECAP deformation with route BC in the volume that was charac-
terized by 3-D EBSD. The tolerance angle selected for estimating the volume
fraction of texture components is 10◦. The value was selected due to the scat-
ter width of the components in the ODF under the constraint of avoiding the
overlap. It can be observed that by increasing the number of ECAP passes
the volume fraction of A∗1E and A∗2E orientations increases continuously from
2-pass ECAP to 8-pass ECAP, opposed to the volume fraction of AE which
decreases with increasing the number of passes. As mentioned before CE is
the second texture component after 2 ECAP passes. The moderate strong CE
texture component after 4 and 8 ECAP passes could be retained CE compo-
nents from the previous passes. Finally to summarize the texture evolution
during ECAP deformation: For the 2-pass ECAP sample a maximum occurs
at an orientation close to AE . Simultaneously the B fiber components, explic-
itly the C component, are present after this level of shear strain (γ = 4). AE
component with a {111} plane positioned parallel to the shear plane is intu-
itively expected to provide the favored systems. This leads to the dominance
of AE component at a shear strain of γ = 4. In the other two samples, namely
4-pass and 8-pass ECAP, the dominant AE component from 2-pass ECAP di-
minishes. At higher levels of strain (γ = 8, γ = 16, 4-pass and 8-pass ECAP,
respectively) the A∗1E and A2E∗ components become stronger.
The loss of the AE component and increase of the A∗1E can be also rationalized
as follow. When the {111} plane normal is parallel to the torsion axis (normal
direction), by increasing the deformation degree to the sample by ECAP the
rotation of the grains continuously occurs and during this rotation the case
comes up with the shear direction lying midway between two of the <110>
95
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.13: Volume fraction of ideal ECAP texture components (table2.2) in
the measured volume via 3-D EBSD measurements for 2-, 4-, and 8-
pass ECAP.
96
5. 3-D Microstructure
Burgers vectors, and perpendicular to the third one. This case matches the
A∗1E component and produces equal double slip. In torsion texture there are
no stable orientations because any particular grain is rotating constantly, the
presence of texture is somehow because of quasi-stationary positions in the
orientation distribution, where grains rotate slowly (102). At BE orientation
occurs also a maximum for the 4-pass ECAP sample. The BE texture compo-
nent is the transition between AE and CE components. Fig. 5.13 shows that
the amount of the AE component increases by the 4-pass ECAP. In route BC
a shear reversal occurs, i.e. the third pass imposes the reverse shear relative
to the first pass and this strain path change is repeated every four passes. The
weakening of the texture is due to the strain path. This leads to weakening
of the texture intensity with increasing the pass number. With increasing the
pass number the orientation density of the main shear component decreases
from 32 for the 2-pass ECAP to 10 for the 8-pass ECAP. Figs. 5.14, 5.15,
5.16, 5.17, 5.18, 5.19, 5.20, 5.21, 5.22 show the 3-D spatial distribution of
A∗1E , CE , AE components for three ECAP samples, namely after 2, 4 and 8
ECAP passes. Elongated grains still prevail even after ECAP passes. The
distribution of the ECAP texture components A∗1E , CE and AE after 8 ECAP
passes is more homogeneous than after 2 and 4 ECAP passes, documenting
the gradual homogenization of the microstructure through an increased num-
ber of ECAP passes. However, pronounced spatial 3-D correlation among
grains of the same orientation do not evolve.
Grain size and grain shape Any polycrystalline material contains grains
of more than one size. We may define a discrete distribution function such
that e.g. n(D0) represents the actual number of grains in the sample of size
97
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.14: 3-D distribution of A∗1E (170.37◦ 90◦ 45◦) / (1 1 8) < 4 4 1 > in the
measured volume after 2 ECAP passes.
98
5. 3-D Microstructure
Fig. 5.15: 3-D distribution of A∗1E (170.37◦ 90◦ 45◦) / (1 1 8) < 4 4 1 > in the
measured volume after 4 ECAP passes.
99
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.16: 3-D distribution of A∗1E (170.37◦ 90◦ 45◦) / (1 1 8) < 4 4 1 > in the
measured volume after 8 ECAP passes.
100
5. 3-D Microstructure
Fig. 5.17: 3-D distribution of CE (45◦ 90◦ 45◦) / (3 3 4) < 2 2 3 > in the
measured volume after 2 ECAP passes.
101
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.18: 3-D distribution of CE (45◦ 90◦ 45◦) / (3 3 4) < 2 2 3 > in the
measured volume after 4 ECAP passes.
102
5. 3-D Microstructure
Fig. 5.19: 3-D distribution of CE (45◦ 90◦ 45◦) / (3 3 4) < 2 2 3 > in the
measured volume after 8 ECAP passes.
103
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.20: 3-D distribution of AE (45◦35.26◦45◦) / (914) < 1115 > in the
measured volume after 2 ECAP passes.
104
5. 3-D Microstructure
Fig. 5.21: 3-D distribution of AE (45◦35.26◦45◦) / (914) < 1115 > in the
measured volume after 4 ECAP passes.
105
5.1. 3-D based microstructure and microtexture characterization
Fig. 5.22: 3-D distribution of AE (45◦35.26◦45◦) / (914) < 1115 > in the
measured volume after 8 ECAP passes.
106
5. 3-D Microstructure
D0. Polycrystalline materials contain such a large number of grains that it is
mathematically and conceptually simpler to treat the grain size as a continu-
ous variable. It is known that the grain size distribution of the nanocrystalline
materials can be well described by a lognormal function (14). A lognormal
distribution has the form
fLN(V) =
∫1√
2V ln V0
exp{12
[ln V
V0
ln V0
]} (5.1)
where V0 and σ are constant parameters describing the median and variance
of the distribution, respectively. For the log normal distribution the mean
grain size is not the most frequent size (median). The mean grain size can be
calculated from the following equation, where Vm is the mean grain size (14):
Vm = exp(ln V0 − σ2) (5.2)
Fig. 5.23 depicts a Gaussian distribution for three 2-, 4- and 8-pass ECAP
microstructures. In this study the grain is defined as volumes in which the
tolerance angle does not exceed over 5◦ and the minimum number of voxels
for defining of the grain is 10 voxels. The arithmetic mean grain size (grain
volume) is 1.22× 109, 1.62× 108 and 6.56× 107 for the microstructures after
2, 4 and 8 ECAP passes, respectively. It demonstrates that the grain size
decreases with increasing the number of ECAP passes. On the other side the
probability-weighted mean grain size (grain volume) is 3.2 × 107, 5.1 × 106
and 8 × 106 [nm]3 for the 2-, 4- and 8-pass ECAP material, respectively. The
probability-weighted mean grain size is decreasing from the 2-pass ECAP
to 4-pass ECAP material. The fitted curve in fig. 5.23 is shifted to the left
(smaller grain volumes) after 4 ECAP passes comparing to the Gaussian curve
for the 2-pass ECAP material which is a demonstration for grain refinement
in the microstructure. Comparing 4 and 8-pass ECAP materials, we observe
that the fraction of the smallest grains in the microstructure decreases after
8 ECAP passes which could be an indication to the fact that the number of
sub-grains in the microstructure is decreasing. If we take the results from fig.
5.23 with the ones form fig. 5.6 , it can be conclude that the smaller grains in
the microstructure after 4 ECAP passes are the sub grains which diminish by
107
5.2. Grain boundary analysis
Fig. 5.23: Grain size distribution in the a) 2-pass, b) 4-pass and c) 8-pass
ECAP Cu-o.17wt%Zr material. The plotted curve is a Gaussian func-
tion (equation 5.2).
increasing the ECAP passe-number and change their character to the grains
surrounded by the high angle grain boundaries. Fig. 5.24 shows the grain
shape in the 2, 4 and 8-pass ECAP samples. The grains after 2 ECAP passes
are mostly elongated which can be referred to the deformation path. These
elongated grains were also reported by other authors (95, 96, 98, 97, 103).
After 4 ECAP passes the fraction of such elongated grains decreases. There
are some equi-axed grains existing beside some retained elongated grains.
The microstructure of the material after 8 ECAP passes is more homogeneous
but some elongated grains can be seen in the microstructure (fig. 5.24).
5.2 Grain boundary analysisGrain boundaries play an important role in different processes such as grain
growth, recrystallization, deformation, etc. One of the most important sights
of the 3-D EBSD measurements are the analysis of the grain boundaries. Such
information is not available from 2-D EBSD data as the grain boundaries
are characterized by 5 parameters, namely the misorientation (3 variables)
and grain boundary plane orientation (2 variables). In this work the grain
108
5. 3-D Microstructure
Fig. 5.24: 300 selected grains (tolerance angle; 5◦, cutoff size: 10 voxels)
in the 3-D reconstructed microstructure of the 8-pass ECAP sample
mapped with an in-plane step size of 50 nm.
109
5.2. Grain boundary analysis
boundary analysis was started with an annealed microstructure. In such mi-
crostructure the grain boundaries are mostly in equilibrium state and the size
of the grains are larger. These all lead to a more reliable analysis to be sure
that the approach for analyzing the grain boundaries from 3-D EBSD data
is reliable and successively will be focused on the grain boundaries of the
deformed structure. In this work we applied 3 different methods to crystal-
lographically quantify interfaces from 3-D and 2-D EBSD data sets, namely,
the line segment method (LS) 8, the triangular surface mesh method (TSM)
and the stereological method. The different approaches are schematically il-
lustrated in fig. 5.25. The LS and the TSM methods were developed for
reconstructing the interfaces in a 3-D microstructure with the aim to obtain
the GBCD function directly from discrete 3-D topological data sets in the
group of Prof. Rollett and Prof. Rohrer at Carnegie Melon University. The
stereological method was developed as a statistical measure for calculating
the GBCD from observations on a 2-D EBSD data set. In the first approach
(line segment method) used for calculating the GBCD, the first step is to re-
construct the grain boundaries as straight line segments ((92, 13)). The OIM
software was used for reconstructing the straight boundaries from the seg-
ment boundaries. The exact approach for building the straight line boundaries
used in the OIM software is described in (104). From this step we obtain a
list of segments for each layer, which includes information about the average
orientation of the grains on either side of the segment in the form of Euler
angles (Bunge notation ϕ1, φ, ϕ2), length of the segment, the angle of the re-
constructed segments, coordinates of the endpoints in microns and an integer
identifier for the right hand and left hand side grains. The lists including in-
formation about the line segments will be used as the input for the software
for calculating the GBCD. The method then obtains the triple junctions by
identifying all sets of three segments sharing the same coordinate of an end
point. These triple junctions in each layer should be matched with the triple
junctions on the adjacent layer. The algorithm identifies the five closest triple
junctions on the adjacent layer and compares the three crystal orientations on
the first layer with the three ones on the adjacent layer. When the disorienta-
tion between the crystal orientations is less than 5◦ a triple line connects the
two triple points identified in the adjacent layers. The grain boundary normal
110
5. 3-D Microstructure
will be then determined by the cross product of two vectors of the boundary
plane. The discrete grain boundary type of this segment is then determined
according to its individual misorientation and boundary normal. Instead of
the analysis of the five-parameter GBCD in five-dimensional space, symme-
try operations are used to confine the analysis to a sub-domain in which the
misorientation parameters vary between 0− π2. This domain, which has a con-
venient shape for discretization, contains multiple copies of the fundamental
zone of misorientations (13) in cubic materials. The plane normal is defined
by two angles, namely, the in-plane angle (φ) and the azimuthal angle (θ).The azimuthal angle varies between 0 − π
2and the in-plane angle between
0 − 2π (for centrosymmetric samples) (12, 90). The cells in the misorienta-
tion space have the same volume, for that the ϕ1, cos(φ) and φ2 are equally
partitioned. There are D3 cells in the misorientation space (fig. 5.26 a). For
each cell in the Euler space there is also a distribution of boundary normal.
There are 4D2 cells in the boundary normal space (fig. 5.26 b). In this case
the phi and cosθ are partitioned so that the area of the cells on the surface of
the hemisphere are equal and in that case the number of cells are 4 × D2. In
the five parameter grain boundary space each cell has the same probability to
be populated (105). The normalized sum of area of boundary planes make up
the GBCD.
In the second approach (stereological method), the grain boundary traces (li j)
and the misorientations in a 2-D EBSD section of a polycrystalline mate-
rial are known. Although the normal of the grain boundary plane (ni jk) is not
known, it is obvious that it belongs to a set of planes that include the boundary
trace in the respective 2-D EBSD section and obeys the condition li j×ni jk = 0,
where ni jk are a set of C unit normals to the possible grain boundary planes.
In fig. 5.25 a, K = 1, 2, 3, 4 are all possible boundary planes which pass
through the boundary trace and obey the condition li j × ni jk = 0. For each
misorientation, sets of ni jk (C cells) are accumulated and weighted according
to the length of the observed boundary trace. If there are N observations of
traces for a specified misorientation, then there will be N correct boundary
normal orientations and N(C-1) incorrect orientations (11, 12). In this kind
of analysis, it is important that the microstructure has the random orienta-
tion with respect to the sample references. To obtain the line length in each
111
5.2. Grain boundary analysis
boundary type, it is important to exclude the incorrect orientations. Accord-
ing to analysis of Saylor et al. (106), if there is a peak in the distribution of
grain boundary planes, it is more probable for the orientations near to this
peak to have incorrectly assigned length than the orientations far from this
peak. By subtracting the incorrectly assigned length, an approximation of the
inhomogeneous distribution is considered. Although the method can serve as
an approximate measure of the interface normal distribution it must be con-
sidered that it is retrieved by a statistical method. However, the calculation of
population of grain boundaries in the five parameter grain boundary space is
performed as explained for the LS method. In the third approach (triangular
surface mesh method), the interfacial areas are discretized into triangular area
sets using a generalized marching cube algorithm by which all lines formed
by the edges of these triangles will be smoothed (92). The smoothing process
is the same grain boundary smoothing in 2-D. In smoothing the grain bound-
aries in 2-D measurements the triple points and in 3-D the quadruple points
are fixed and the grain boundary is considered as a string of edges. From
the starting node (triple point) a line will be drawn to the midpoint of the next
edge. If the distance from the previous node is less than the defined threshold,
a line will be drawn to the next edge. This process continues until the distance
is larger than the threshold and then the line to the previous edge is selected as
the new smoothed boundary and all the nodes are moved to the qui-distance
points on the smoothed line and the end point will be the start point for further
smoothing. Smoothing of the boundaries in 3-D includes smoothing of triple
and quadruple lines, lines on the surface of the microstructure and smoothing
lines on the grain boundary planes. The marching cubes method is a standard
iso-surface grid generation algorithm (107) and generates a conformal trian-
gular surface mesh that represents the internal interface structure of the mate-
rial. In both, the Line Segment and the Triangular Surface Mesh methods, it
is necessary to properly align the layers before reconstructing and calculating
the GBCD. It is assumed that the successive layers are parallel to each other
and there is no rotation between layers. There are two steps for aligning the
layers. In the first step of alignment the main assumption is that the distance
between layers is smaller than the grain size and the additional assumption is
that the orientation changes within a grain may be neglected (91).The primary
112
5. 3-D Microstructure
alignment code minimizes the disorientation between corresponding voxels
between adjacent layers (91). The number of neighboring voxels contribut-
ing to the calculation of average disorientation was 2 for coarse registration
and 8 for fine registration. After disorientation calculations are performed
there will be a sharp minimum in the average disorientation as a function of
x and y directions. In the secondary alignment a rigid shift is performed so
that the average triple line direction is parallel to the surface. It was shown
by Rohrer et al. (13) that the displacements in the y direction are lager than
the ones on x direction. This was explained by the tilting of the sample by
70◦ which magnifies the error by the factor 3. This alignment procedure was
performed in the way that the triple point on every second layer were matched
together. (13)
5.2.1 Grain boundary character distributionExperiments
The experiments were conducted using a Cu-0.17wt%Zr alloy. The samples
were processed by ECAP at room temperature using 8 passes via route BC .
After ECAP deformation the samples were annealed at 650◦C for 10 minutes.
The mapping was performed using a dual-beam system for 3-D EBSD in a
Zeiss XB1560 microscope. The FIB was operated at an accelerating voltage
of 30 kV and 2 nA and 500 pA beam for coarse and fine milling, respectively.
The spacing between subsequent slices was 170 nm. The volume analyzed
was 28 × 28 × 17 [μm]3. For this study, on a large sample section which
included 86000 2-D boundary line segments, a 2-D EBSD measurement was
performed.
Results and discussion
Fig. 5.27 shows the 3-D microstructure of the sample after 8 ECAP passes
and subsequent annealing at 650◦C for 10 minutes. The microstructure is re-
constructed using Paraview software, an open source visualization software
113
5.2. Grain boundary analysis
Fig. 5.25: Schematic representation of a) the statistical stereological method
(from 2-D EBSD data) and the analysis of interfaces from 3-D EBSD
data, b) line segment method, and c) triangular surface mesh method.
li j are the grain boundary trace segments in a 2-D EBSD data set; ni jk
are the unit normals to the possible grain boundaries; k is the possible
grain boundary plane; and gi is crystallographic grain orientation (108).
114
5. 3-D Microstructure
Fig. 5.26: The parameterization of λ(δg, n) into a) three lattice misorienta-
tion parameters and b) two boundary plane orientation parameters, the
spherical angles are used to parameterize the boundary plane orienta-
tion. The range of boundary plane orientation is so parameterized that
all the cells have the same width in φ and cosθ and the same area on
the surface of the hemisphere. In the misorientation space there are
D3 cells and for each of these cells, there is a hemisphere of boundary
plane normals with 4D2 cells. (105)
115
5.2. Grain boundary analysis
package (109). The color indicates the crystallographic directions parallel to
the extrusion direction (ED) using an inverse pole figure code. The distribu-
tion of the grain boundary planes in the crystal reference frame at Σ3 interface
(60◦@[111]) in CuZr after 8 ECAP passes and subsequent annealing at 650◦Cfor 10 minutes is shown in fig. 5.28. The symbol Σ defines the volume of the
elementary cell of the coincidence site lattice relative to the volume of the
elementary cell of the underlying crystal lattice.
The Coincidence Site Lattice (CSL) concept is a theoretical method for
identifying specific misorientations that bring a certain fraction of lattice sites
into coincidence when one copy of the lattice is rotated relative to its origi-
nal position [29]. We used a maximum allowable deviation from the ideal
Σ3 boundary of 8.67◦ according to Brandon criterion (110). In this study
we compare the results of the discretization of orientation space into 9 bins
(corresponding to 10◦ resolution) and 11 bins (corresponding to 8.18◦ resolu-
tion). The later discretization matches Brandon’s criterion reasonably closely
(110). A pure twist configuration occurs when the grain boundary normal
is parallel to the misorientation axis. Σ3 (60◦@[111]) boundaries with {111}planes on both sides, are referred to as coherent twin boundaries. The co-
herent twin boundary inverts the regular A-B-C stacking sequence of close
packed {111} FCC layers at the twin boundary plane. Since the nearest and
the next-nearest-neighbor atom positions are unchanged, the energy of coher-
ent twin boundaries is very small (111). Since copper has a low stacking fault
energy, the formation of annealing Σ3 boundaries is favorable. Due to this
fact, we expect a high fraction of coherent twin boundaries in the material.
Fig. 5.29 represents the GBCD function of the Σ3 interface as calculated
from the Line Segment method. In this figure a relatively strong peak at the
Σ3 pure twist boundary position (indicating a coherent twin structure) can
be observed. The maximum peak intensity (marked by a red triangle in fig.
5.29) is about 230 multiples of the random distribution (MRD), when the
space is discretized in 9 bins per 90◦, while the maximum peak intensity for
the coherent twin is about 1100 MRD when the space is discretized into 11
116
5. 3-D Microstructure
Fig. 5.27: 3-D microstructure of the Cu-0.17wt%Zr sample after 8 ECAP
passes and subsequent annealing at 650◦C for 10 minutes as obtained
from 3-D EBSD (92, 12). The color code indicates the crystal direc-
tions parallel to ED (extrusion direction). The alignment of the 2-D
slices is based on minimizing the disorientation between matching vox-
els in adjacent 2-D EBSD layers (91)
.
117
5.2. Grain boundary analysis
Fig. 5.28: a) Misorientation angle relative fraction distribution, b) relative
areas of the boundary plane distribution, of the sample after 8 ECAP
passes with subsequent annealing at 650◦C for 10 minutes. The red
triangle marks the [111] direction (triangular surface mesh method).
118
5. 3-D Microstructure
bins per 90◦. It is apparent that the angular discretization scheme influences
the results. Especially in cases such as the Σ3 and higher order coincidence
grain boundaries (13) it is, hence, sensible to prefer discretizations that are
consistent with the deviations suggested by the Brandon criterion. However,
it must also be noted that the finer discretiazation requires more independent
observations to populate the bins. We should also consider that the cells in the
misorientation sub-domain are parameterized by an angular portion set by ϕ1,
cos(φ), ϕ2. The ideal Euler angles of the twin misorientation are ϕ1 = 45◦,Φ = 70.5◦ and ϕ2 = 45◦. For the discretization of 9 bins per 90◦, the limits
of each bin lie at the intervals of 1/9. For the Σ3 twins the cos(φ) amounts
to 3/9 and falls on the border between the bins. Hence, the intensity of the
twin may splits into multiple bins and may appear lower than expected. Fig.
5.30 shows the GBCD function as calculated from the stereological method.
In this approach a 2-D EBSD measurement was performed on a large sample
section.The result reveals that all Σ3 boundaries are located on the coherent
twin boundary planes and the intensity of Σ3 on all other planes is very small.
The maximum plane density of the coherent twin boundaries obtained from
this stereological approach is about 8000 MRD for the case where orientation
space was discretized into 11 bins per 90◦ (fine angular resolution of 8.18◦according to Brandon’s criterion). In contrast, the results obtained from the
Line Segment method (Fig. 5.29) and the Triangular Surface Mesh method
(Fig. 5.31) show that, although a strong peak of the Σ3 grain boundary ap-
pears at the expected position, not all the Σ3 boundaries are found in an exact
coherent twin configuration.
Fig. 5.31 shows the GBCD results obtained from triangulation of the inter-
facial areas after applying the marching cube algorithm. In this analysis the
maximum intensity of the Σ3 boundaries is about 230 multiples of random
distribution (MRD) for a discretization of 9 bins per 90◦, while the maximum
peak intensity for the coherent twin with the discretization of 11 bins per 90◦is about 800 MRD. There are slight differences in the maximum and mini-
mum peak intensities between the Line Segment and the Triangular Surface
Mesh methods. However, both 3-D analysis methods reveal that not all the
Σ3 boundaries are coherent twin boundaries (Fig. 5.32).
119
5.2. Grain boundary analysis
Fig. 5.29: Grain boundary analysis according to the Line Segment method
obtained from 3-D EBSD data for a sample after 8 ECAP passes plus
subsequent annealing at 650◦C for 10 minutes. The results are plot-
ted as a grain boundary plane distribution function for the Σ3 inter-
faces. a) orientation space is discretized in 9 bins per 90◦ (coarse an-
gular resolution(10◦)), b) orientation space is discretized in 11 bins per
90◦ (fine angular resolution(8.18◦)). The red triangle marks the co-
herent twin boundaries. Note the different scaling, corresponding to
the stronger peak for the higher resolution binning. Both discretization
schemes reveal a strong maximum for the coherent Σ3 (60◦@[111])
grain boundary (i.e. with a {111} grain boundary plane).
120
5. 3-D Microstructure
Fig. 5.32 shows the maximum and minimum intensities of the Σ3 grain
boundaries in MRD for all three approaches, i.e. stereology, triangular sur-
face mesh, and line segment analysis. The data reveal three main points. First,
the maximum and minimum intensities for Σ3 depend for all three different
analysis methods on the angular binning scheme. Second, the Triangular Sur-
face Mesh and the Line Segment methods which are both obtained directly
from generic 3-D EBSD topological data sets, provide consistent results. The
quite large discrepancy between the stereology approach and the two other
methods regarding the ratio of the coherent versus non-coherent Σ3 interfaces
is attributed to the influence of preferred textures. The statistical stereological
approach might suffer from the fact that once a peak in a real grain orienta-
tion distribution occurs (preferred crystallographic texture), other orientations
that are close to this maximum in the orientation density may have a more in-
correctly assigned length contribution to the interfaces. In the subsequent
calculation of the GBCD, the background corresponding to all erroneously
accumulated observations is subtracted from the distribution. This will be
done under assumption of a random crystal orientation distribution. How-
ever, the presence of a preferred <111> texture in the current case leads to an
overestimation of the background and, hence, to an incorrect normalization
(large subtraction). This lowers the population of incoherent boundaries but
has less effect on the intensity of the maximum that is located at the coherent
Σ3 interface. The other two analysis approaches are not based on statistics
(as the stereological method) but on the direct topological analysis of every
single existing boundary in the microstructure. Hence, their analysis results
do not suffer from the statistical effects explained above but they are more
sensitive to the alignment and possible distortion effects between neighbor-
ing 2-D EBSD maps that are used for the topological reconstruction (13).
Such misalignments may lead to a broadening effect of the boundary plane
orientation distribution away from the peaks and to a drop in the maximum
(located at the coherent twin boundaries). Instead the fraction of incoherent
Σ3 interfaces is increased. Based on the results from ref. (13), the 3-D analy-
sis methods hence typically underestimate the most populous grain boundary
plane orientations and overestimate the neighboring plane orientations.
The intensity of the coherent twin boundaries in the Triangular Surface Mesh
121
5.2. Grain boundary analysis
approach is slightly lower than the intensity from the Line Segment method.
This may be a consequence of imperfect smoothing performed after triangu-
lation of the interfaces. Fig. 5.33 underlines these comments as it shows the
area fractions of the total Σ3 twin boundary populations and of the coherent
Σ3 twin boundaries obtained from the three approaches. Indeed the density of
the coherent twins is much larger in the Stereological analysis as opposed to
the small density found from the two discrete 3-D methods (Fig. 5.33). When
contrasting this result with the density of all Σ3 (60◦@[111]) grain boundaries
(counting both, coherent and incoherent interfaces) the three methods deliver
comparable values (fig. 5.33).
Besides the discussion of these differences in the topological robustness of the
three algorithms also symmetry aspects must be considered when aiming at
extracting meaningful information from grain boundary character distribution
functions: If in a cubic system the five angular parameters that characterize a
grain boundary are measured at a resolution of 10◦, there are approximately
6561 distinguishable grain boundaries. One angular sub domain is 1/64thof the entire range. Crystal symmetry effects result in various values of in-
distinguishable δg values (misorientations). In a bicrystal there are 2 × 242
equivalent such misorientations. It should also be considered that it is arbi-
trary whether the grain boundary normal points into the first crystal or into
the second crystal. This adds an additional factor of 2 to the symmetrically
equivalent boundaries so that we obtain 2 × 2 × 242(2304). This means that
there are (2304/64) 36 symmetrically equivalent boundaries in each sub do-
main. If the sub domain is discretized in 9 bins per 90◦, then the number of
cells of equal volume will be 4×95. Thus for a discretization of 9 bins per 90◦the number of distinguishable boundaries is approximately 6561(4 × 95/36).
If the resolution is reduced to 8.18◦, we obtain about 17894 (4 × 115/36) dis-
tinguishable cells. Due to the equal volume of the cells, the value in each
cell is given in terms of MRD. The area fraction of specified grain boundaries
can be calculated by dividing the MRD value by the number of distinguish-
able cells in the sub domain. For example the area fraction of coherent twin
boundaries from the stereological approach is about 44% (8 000/17 894) for
the discretization of 11 bins per 90◦.
122
5. 3-D Microstructure
Fig. 5.30: Grain boundary analysis according to the statistical stereological
method from 2-D EBSD data plotted for a sample after 8 ECAP passes
plus subsequent annealing at 650◦C for 10 minutes. The results are
plotted as a grain boundary plane distribution function for the Σ3 in-
terfaces. a) orientation space is discretized in 9 bins per 90◦ (coarse
angular resolution(10◦)), b) orientation space is discretized in 11 bins
per 90◦ (fine angular resolution(8.18◦)). The red triangle marks the co-
herent twin boundaries. Note the different scaling, corresponding to
the stronger peak for the higher resolution binning. Both discretization
schemes reveal a strong maximum for the coherent Σ3 (60◦@[111])
grain boundary (i.e. with a {111} grain boundary plane).
123
5.3. Conclusion
Fig. 5.31: Grain boundary analysis according to the Triangular Surface Mesh
method obtained from 3-D EBSD data for a sample after 8 ECAP
passes plus subsequent annealing at 650◦C for 10 minutes. The results
are plotted as a grain boundary plane distribution function for the Σ3
interfaces. a) orientation space is discretized in 9 bins per 90◦ (coarse
angular resolution(10◦)), b) orientation space is discretized in 11 bins
per 90◦ (fine angular resolution(8.18◦)). The red triangle marks the co-
herent twin boundaries. Note the different scaling, corresponding to
the stronger peak for the higher resolution binning. Both discretization
schemes reveal a strong maximum for the coherent Σ3 (60◦@[111])
grain boundary (i.e. with a {111} grain boundary plane).
5.3 ConclusionThe microtexture analysis of the ECAPed samples from the 3-D EBSD mea-
surements revealed nearly the same results of the microtexture evolution in
124
5. 3-D Microstructure
Fig. 5.32: Maximum and minimum intensity values of the Σ3 GBCD (grain
boundary character distribution) functions presented above in MRD
(multiples of random) for the three topological approaches: stereol-
ogy (statistical), triangular surface mesh (discrete), and line segment
analysis (discrete). The maximum is at the coherent Σ3 (60◦@[111])
grain boundary (i.e. at the {111} grain boundary plane).
125
5.3. Conclusion
Fig. 5.33: Area fraction of a) Σ3 twin boundaries, b) Σ3 coherent twin bound-
aries in Cu-0.17wt%Zr after 8 ECAP passes and subsequent annealing
at 650◦ C for 10 min from three different approaches: stereological ap-
proach, triangular surface mesh method, line segment method. (GBCD
stands for Grain Boundary Character Distribution.)
126
5. 3-D Microstructure
the microstructure studied by X-ray diffraction. For the 2-pass ECAP sample
a maximum occurs at an orientation close to AE . AE component with a {111}
plane positioned parallel to the shear plane was intuitively expected to pro-
vide the favored systems. In the other two samples, namely 4-pass and 8-pass
ECAP, the dominant AE component from 2-pass ECAP diminishes. At higher
levels of strain (γ = 8, γ = 16, 4-pass and 8-pass ECAP, respectively) the A∗1Eand A2E∗ components become stronger. Real grain size (grain volume) and
grain shape of the ECAPed samples which were analyzed are among the in-
formation which could not be obtained rom the 2-D EBSD measurements.
A correlation between the distribution of the ECAP texture components and
their shape with the ECAP-pass number was existing. With increasing the
ECAP-pass number the texture components were distributed more homoge-
neous and the form of the grains were developed to a more globular equi-axed
shape.
The crystallographic character of the grain boundary planes was determined
using three different methods, namely, the line segment method, the stere-
ological method, and the triangular Surface Mesh method. The statistical
Stereological approach showed that practically all Σ3 boundaries are coher-
ent twin boundaries, i.e. they are bounded by 111 planes on either side. The
results from two other direct topological (3-D) approaches, namely the Line
Segment and the Triangular Surface Mesh method, yielded different results.
They revealed that, although the maximum peak of the grain boundary plane
distribution function for Σ3 also occurs at the coherent twin boundary posi-
tion, not all the Σ3 grain boundaries were coherent. Both types of analysis
methods contain certain inaccuracies. The 3-D analysis is sensitive to the ex-
actness in the alignment between neighboring 2-D EBSD layers from which
the topological reconstruction proceeds. The effect manifests itself by un-
derestimating the populous boundaries and overestimating the neighbor ori-
entations. In the statistical stereology approach, the occurrence of crystallo-
graphic texture effects may artificially lower the population of the incoherent
boundaries, due to which the analysis of the 5D space gain GBCD of the
textured materials produced via SPD methods is favorable.
127
Summary
The first part of the study was dedicated to investigate the recrystallization
behavior of the samples subjected to high levels of strain via high pressure
torsion. The deformed structure revealed the simple shear texture components
of the FCC materials. The strongest texture components with increasing the
strain level kept the same character from strain levels of about 9. The grain
size decreased at the first increasing levels of the strain and then reached the
saturation in refinement of the microstructure. The microstructure evolution
of the heat-treated samples showed that there were some grains, growing dis-
continuously during heat treatment of the samples. Due to the high fraction
of high angle grain boundaries, it was expected that the material shows ho-
mogenous changes of microstructure during heat treating, which was not the
case. Accordingly the stored energy evolution depicted that the stored energy
decreases during annealing processes. The texture results demonstrated the
dominance of the B component and B components in the annealed state. The
stored energy of each texture component existing in the deformed microstruc-
ture was approximated using the kernel average misorientation, however there
was no correlation between the stored energy of the texture components and
their appearance during heat treatment. A correlation between the grain size
and the stored energy was observed. During annealing of the samples the
larger grains yielded the smallest stored energy. This could be explained by
the fact that grains reducing their stored energy grow in the deformed mi-
crostructure and develop a bimodal structure. The driving force for formation
of these grains was obtained most probably from the stored energy of the
129
dislocations. This can be an indication of primary recrystallization. But the
preferable domination of specific texture components was not related to their
stored energy but is probably caused by the character of grain boundaries.
Since the driving force for the discontinuous grain growth and primary re-
crystallization is in the same order of magnitude, it can be concluded that
both processes are active during heat treatment of the strongly strained sam-
ples.
In the second part of this study the 3D microstructure, microtexture and the
grain boundary structure of the UFG material produced by equal channel an-
gular pressing were studied. The grain volume of the ECAPed samples de-
creased with increasing the number of ECAP passes, simultaneously by de-
creasing the grain size, the grain shape was developing to a more equi-axed
shape. The orientation distribution function obtained from the 3D EBSD data
sets were compared withe ones from X-ray diffraction method. here were
some deviations revealed which were attributed to the fact the ECAP process
does not lead to a homogenous deformation but to texture gradients through
the thickness. While the 3D EBSD data provide a through -thickness integra-
tion of the texture, the XRD data are surface sensitive. The strongest texture
component after 2 ECAP passes was the AE component, while the A∗1E and
A2E∗ components become stronger for the sample after 4 and 8 ECAP passes.
It could be observed that the samples processed with lower number of ECAP
passes, namely 2 and 4, showed more pronounced texture gradients than the
sample which was processed by 8 ECAP passes. No pronounced spatial 3D
correlations among grains of the same orientation was evolved. The relation-
ship between the local texture, grain shape, texture component connectivity
were among the information obtained form tomographic method for charac-
terization of the ECAP material.
The crystallographic character of the grain boundary planes was determined
using three different methods, namely, the line segment method, the stere-
ological method, and the triangular Surface Mesh method. The statistical
Stereological approach showed that practically all Σ3 boundaries are coher-
ent twin boundaries, i.e. they are bounded by {111} planes on either side.
The results from two other direct topological (3D) approaches, namely the
Line Segment and the Triangular Surface Mesh method, yielded different re-
sults. They revealed that, although the maximum peak of the grain boundary
plane distribution function for Σ3 also occurs at the coherent twin boundary
position, not all the Σ3 grain boundaries were coherent. Both types of anal-
ysis methods contain certain inaccuracies. The 3D analysis is sensitive to
the exactness in the alignment between neighboring 2D EBSD layers from
which the topological reconstruction proceeds. The effect manifests itself
by underestimating the populous boundaries and overestimating the neighbor
orientations. In the statistical stereology approach, the occurrence of crys-
tallographic texture effects may artificially lower the population of the inco-
herent boundaries, due to which the analysis of the 5D space gain boundary
GBCD of the textured materials produced via SPD methods is favorable.
Zusammenfassung
[ngerman] [german]babel Im ersten Teil dieser Arbeit wurde das Rekristal-
lizationsverhalten von ultra-fine Körniger Cu-0.17wt%Zr untersucht. Das
Material wurde anhand “High Pressure Torsion” Verfahren hochgradig bis
zur äquivalenten Dehnung von etwa 27 verformt. Im verformten Zustand
haben sich die idealen Schertexturkomponenten von FCC Materialien en-
twickelt. Die stärkste Texturkomponente hat seinen Charakter mit steigen-
der Verformung nicht geändert. Die Korngröße hat zuerst abgenommen und
schliefllich hat die Mikrostruktur eine Sättigung der Kornfeinung erreicht.
Die Mikrostruktur von verformten Werkstücken haben über 70% (Flächenan-
teil) Großwinkelkorngrenzen. Es wurde erwartet, dass innerhalb Mikrostruk-
tur von verformten Werkstücken mit über 70% Flächenanteil an Großwinkelko-
rngrenzen, während der Wärmebehandlung, eine homogene Wachstum aus-
gesetzt wird. Es wurde dagegen beobachtet, dass einige Körner diskontinuier-
lich gewachsen sind und eine bimodale Mikrostruktur entstanden ist. Die En-
twicklung der geschätzten gespeicherten Energie von Versetzungen hat eine
Abnahme der gespeicherte Energie während der Wärmebehandlung dargestellt.
Ebenfalls wurde beobachtet, dass die große Körner in der Mikrostruktur niedri-
gere gespeicherte Energie besitzen. Dies deutet daraufhin, dass die gespe-
icherte Energie der Körner mit Wachstumsprozess abnahm, was eine Hinweis
auf der primären Rekristallisation ist. Anderseits zeigte die Texturentwick-
lung von geglühten Werkstücken, dass die B and B Komponenten die stärkste
Orientierungen waren. Die Entwicklung der geschätzten gespeicherten En-
ergie von den beiden dominanten Texturkomponenten war sehr ähnlich der
133
Entwicklung von anderen Texturkomponenten in der Mikrostruktur. Das be-
deutet, dass die gespeicherte Energie von diesen beiden Texturkomponenten
nicht die Ursache deren Auftreten und Dominanz während der Wachstum-
sprozess war, sondern die Charakter von deren Korngrenzen. Es könnte aus-
geschlossen werden, dass während der Wärmebehandlungsprozess sowohl
die primäre Rekristallization als auch das diskontinuierliche Wachstum ak-
tive Prozesse waren. In zweiten Teil dieser Arbeit wurde die Mikrostruk-
tur und Korngrenzencharakter von ultra-fine körnigen Cu-0.17wt%Zr, ver-
formt anhand “Equal Channel Angular Pressing”, in 3-Dimensional unter-
sucht. Es wurde beobachtet, dass das Volumen von ECAP Proben mit steigen-
der ECAP-Durchgang abnahm und der Kornform sich in eine globulare Form
entwickelt hat. Die Orientierungsverteilungsfunktion von ECAP Proben berec-
hnet aus 3D EBSD wurde mit Orientierungsverteilungsfunktion berechnet aus
Röntgenbeugungsmethode verglichen. Es wurde Abweichungen in Ergebnis-
sen von beiden Methoden beobachtet. Diese Beobachtung ist auf die Textur-
gradienten durch die Dicke der ECAP proben und inhomogene Mikrostruk-
tur von diesen Proben zurückzuführen. Die 3D EBSD Methode kann In-
formationen über die Texturgradienten durch die Dicke der Probe beschaf-
fen. Es wurde aus Ergebnissen von 3D EBSD Methode über Textur fest-
gestellt, dass Die Texturgradienten in ECAP-Proben nach 2 und 4 ECAP-
Durchgängen stärker waren als die Texturgradienten in der Probe nach 8
ECAP-Durchgängen. Die stärkste Orientierung nach 2 ECAP Durchgängen
war die AE Komponente während die A∗1E und A∗2E die stärkste Texturkom-
ponente nach 4 und 8 ECAP Durchgänge waren. Es hat sich keine räumliche
Korrelation zwischen den Körnern gleicher Orientierung in der Mikrostruktur
entwickelt. Die kristallographische Charakter von Korngrenzenebenen wurde
anhand drei Methoden, nämlich “Stereological”, “Line Segment” und “Trian-
gulation Surface Mesh” Methoden, analysiert. Die stereographische Methode
zeigte, dass alle Σ3 Korngrenzen, kohärente Korngrenzen sind. Die Ergeb-
nisse von den beiden topologischen Methoden (“Line Segment” und “Trian-
gulation Surface Mesh”) haben dargestellt, dass die kohärente Σ3 Korngren-
zen meist belegte Korngrenzenebenen waren aber nicht alle Σ3 Korngrenzen
die kohärente Korngrenzen sind. Alle drei Methoden haben ihre eigene Un-
genauigkeit. Die topologischen Methoden sind sehr empfindlich gegenüber
Alignmentsverfahren von benachbarten 2D-EBSD Schichten, woraus die 3D
topologische Rekonstruktion der Mikrostruktur fortgesetzt wird. In diesen
Methoden kann eine Unterschätzung der Intensität von höchst belegten Ebe-
nen und überschätzung der Intensität der benachbarten Orientierungen her-
vorgerufen werden. In stereographische Methode eine Absenkung der Inten-
sität von nicht Kohärente Korngrenzen wegen der Präsenz von Textur her-
vorgerufen wird. In texturierten, ECAP verformten Materialien wird die 3D
topologische Methode für die Analyse des Konrgrenzencharakters bevorzugt.
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Lebenslauf (CV)
Persönliche Daten
Name: Anahita Khorashadizadeh
Geburtsdatum: 11. Juni 1977
Geburtsort: Teheran
Schulbildung (Education)
1983–1988 Grundschule, Teheran
1988–1991 Mittelstufe, Tehran
1991–1995 Oberstufe, Tehran
Studium (Academic studies)
1996–2001 B.Sc. im Metallurgie und Werkstofftechnik, Teheran Universität
2003–2007 M.Sc. im Metallurgie und Werkstofftechnik, RWTH Aachen
Masterarbeit “Untersuchung der Textur- und
Mikrostrukturentwicklung einer ECAP verformten
CuZr- Legierung”
Berufliche Tätigkeit (Professional experience)
2001–2002 Assistent Inspektor, Iranian Inspection Co.
“Inspektion der Gasrohrleitung der iranischen Nationalbibliothek
Inspektion von Wärmeaustausche, Gas Speicherbehälter
und Druckbehälter”
2003–2007 Studentische Hilfskraft, RWTH Aachen Institut für Metallkunde
und Metallphysik (IMM)
Seit 2007 Wissenschaftliche Mitarbeiterin, Max-Plank-Institut für
Eisenforschung GmbH Düsseldorf